## Mathematics Presentation for Class 12

Book 1 - mathematics, chapter 1: relations and functions, chapter 2: inverse trigonometric function, chapter 3: matrices, chapter 4: determinants, chapter 5: continuity and differentially, chapter 6: applications of derivatives, book 2 - mathematics, chapter 7: integrals, chapter 8: applications of integrals, chapter 9: differential equations, chapter 10: vector algebra, chapter 11: three dimensional geometry, chapter 12: three dimensional geometry, chapter 13: three dimensional geometry.

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## NCERT solutions for class 12 Maths - PowerPoint PPT Presentation

## NCERT solutions for class 12 Maths

Ncert solutions for class 12 maths: students are preparing for the board exam in class 12. this year is considered as the year of career where there is huge opportunity lined up based on their performance. class 12 maths are crucial during the preparation of board exam. therefore, ncert solutions for class 12 is prepared for the student to practice any difficult questions. syllabus for maths is shared in this article along with the solutions. ncert solutions are even useful for preparation of competitive engineering exams. cbse ncert solutions help students in securing good cgpa. you can download the ncert solutions and practice for the exams. – powerpoint ppt presentation.

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## GRADE 12 – MATHEMATICS – 5 POWERPOINT LESSONS

Animated, engaging core content of various topics.

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## Resource Description

All the equations, sketches, drawings and diagrams were created in PowerPoint and are fully and easily editable by anyone – this ensures that the lessons are adaptable for future use. This product is also sold by Teacher911.

STRICTLY SET ACCORDING TO CAPS TOPICS: 1. Exponential & logarithmic Functions 2. Finances, Growth & Decay 3. Functions & Inverses 4. Number Patterns, Sequences & Series 5. Trigonometry

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## Cengage Maths Solutions Class 12 Integrals - Calculus

Mar 25, 2021

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Cengage Maths Solutions Class 12 Integrals PDfs provides accurate solutions to practice before your final exam. Students can study this comprehensive Cengage Maths PDf Solutions on Integrals and its various sub-topics for effective exam preparation. The Cengage 12 PDF solutions help the student to swiftly practice and revise the important concepts just before the annual exam to score high marks in maths.<br>For more such video solutions/Pdf solution, visit https://doubtnut.com and clear your doubt instantly.

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CENGAGE / G TEWANI MATHS SOLUTIONS CHAPTER INTEGRALS || CALCULUS Download Doubtnut Today Ques No. Question CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration (1 + x)3 Evaluate: ∫ dx. 1 √x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration ∫2x+1− 5x−1 10x Evaluate 2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration Evaluate: ∫sec2xcosec2xdx. 3 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration 1 − cosx Evaluate ∫ dx. 4 1 + cosx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration 1 Evaluate: ∫ dx 5 1 + sinx Watch Free Video Solution on Doubtnut

CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration 1 − cos2x ∫tan−1{√( )} Evaluate: 6 1 + cos2x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration secx Evaluate: ∫ dx. 7 secx + tanx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration ∫(secx + tanx)2dx Evaluate: 8 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration Evaluate : ∫(1 − cosx)cosec2xdx 9 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration Evaluate: ∫amxbnxdx 10 Watch Free Video Solution on Doubtnut

CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration tanx Evaluate: 11 dx secx + tanx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration x4 1 If ∫ dx = f(x) + c, the ≠ valuate∫ dx. 12 x + x5 x + x5 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration (x3+ 8)(x − 1) If ∫ 13 dx x2− 2x + 4 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration sin3x + cos3x Evaluate: ∫ dx 14 sin2xcos2x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration 15 Evaluate: `inttan^(-1)(secx+tanx)dx ,-pi/2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration 16 + 2

x + 2 Evaluate: ∫ dx. (x + 1)2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration 8x + 13 Evaluate ∫ dx 17 √4x + 7 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration Evaluate ∫sin3xdx 18 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration Evaluate ∫sin2xsin3xdx. 19 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration dx Evaluate: ∫ 20 (2x − 7)√(x − 3)(x − 4) Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration

1 21 Evaluate: ∫ dx. √3x + 4 − √3x + 1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration dx x Find the values of such that ∫ = tan( + a) + b aandb 22 1 + sinx 2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration 3 x2− 1 1 2 Evaluate: ∫(x + ) ( )dx 23 x2 x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration x Evaluate: ∫ dx 24 √x + 2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration sec2x Evaluate: ∫ 25 dx 3 + tanx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration −x x−

ex− e−x Evaluate: ∫ 26 dx ex+ e−x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration 1 − tanx Evaluate: ∫ dx 27 1 + tanx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration 1 Evaluate: ∫ dx. 28 1 + e−x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration sin2x Evaluate: ∫ dx. 29 a2sin2x + b2cos2x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration tanx log( ) 2 Evaluate: ∫ 30 dx sinx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration

√2 + logx 31 Evaluate: ∫ dx x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration Evaluate: ∫tan4xdx 32 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration Evaluate: ∫(tanx − x)tan2xdx 33 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration 3 (sin−1x) Evaluate: ∫ 34 dx √1 − x2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration x + 1 )(x + logx)2dx Evaluate: ∫( 35 x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration

36 √tanx Evaluate: ∫ dx. sinxcosx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration cotx Evaluate: ∫ dx 37 √sinx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration dx Evaluate: ∫ 38 3 x2(x4+ 1) 4 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Elementary Integration dx Evaluate: ∫ 39 √2ax − x2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions e3x+ e5x Evaluate: ∫ dx 40 ex+ e−x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫tan2xsin2xdx 41 Watch Free Video Solution on Doubtnut

CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions cosx − sinx Evaluate: ∫ (2 + 2sin2x)dx 42 cosx + sinx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫cosec4xdx 43 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions sin2x Evaluate: ∫ 44 (a + b cosx)2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫sinxcosxcos2xcos4xcos8xdx 45 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions (1 + 1nx)5 Evaluate: ∫ 46 dx x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions

cos2x − cos2θ 47 Evaluate: ∫ dx cosx − cosθ Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions x3 Evaluate: ∫ dx 48 x + 1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions dx Evaluate: ∫ 49 √x + √x − 2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫(1 + 2x + 3x2+ 4x3+ )dx, ( < |x| < 1) 50 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1n(1nx) Evaluate: ∫ dx, (x > 0) 51 x1nx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions

dx Evaluate: ∫ 52 x + xlogx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫secpxtanxdx 53 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions ∫sin6x cos8x Evaluate: 54 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫sin2xd(tanx) 55 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1

1 Evaluate: ∫ dx 56 √3sinx + cosx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ dx 57 sin(x − a)sin(x − b) Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫{1 + 2tanx(tanx + secx)) dx 2 58 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions dx Evaluate: ∫ 1 59 (1 + sinx) 2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions dx Evaluate: ∫ 60 cosx − sinx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions

sinx 61 Evaluate: ∫ dx sin(x − a) Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫tan3xdx 62 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫sin(ex)d(ex) 63 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫cos3x√s ∈ dx 64 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions sin2x Evaluate : ∫ dx 65 a2+ b2sin2x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions

66 ∫(222x (22x)(2x))dx Evaluate: Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions dx Evaluate: ∫ 67 1 1 x + x 2 3 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions e2x− 1 Evaluate: ∫ dx. 68 e2x+ 1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 2x −√sin−1x Evaluate: ∫ dx. √1 − x2 69 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions e√xcos(e√x) Evaluate: ∫ 70 dx √x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions tanx Evaluate: ∫ dx 71 a + btan2x Watch Free Video Solution on Doubtnut

CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions ex(1 + x) Find ∫ dx 72 cos2(xe2) Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions sin3xdx Evaluate: ∫ 73 (cos4x + 3cos2x + 1)tan−1(secx + cosx) Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ dx 74 (x2+ 2x + 2)2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions x x)1nxdx. e x Evaluate: ∫(( ) + ( ) 75 x e Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ 76 √e5x(e2x+ e− 2x)34 Watch Free Video Solution on Doubtnut

CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 77 Find: ∫sin5xdx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Find: ∫sin3xcos5xdx 78 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions dx Find: ∫ 79 sinxcos3x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫sin2xcos2xdx 80 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions x2tan−1x3 Evaluate: ∫ dx 81 1 + x6 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions

∫√xdx 1 + x 82 Evaluate: Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions cotx Evaluate: ∫ dx 83 √sinx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions dx Evaluate: ∫ 84 x +√x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions dx Evaluate: ∫ 85 9 + 16sin2x Watch Free Video Solution on Doubtnut

CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions e2x− 2ex Evaluate: ∫ dx 86 e2x+ 1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions ax3+ bx Evaluate: ∫ dx 87 x4+ c2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions dx Evaluate: ∫ 88 2 2 x (1 + x ) 3 3 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions −1dx Evaluate: ∫e3logx(x4+ 1) 89 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions ∫secxdx √cos2x Evaluate: 90 Watch Free Video Solution on Doubtnut

CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫sin3xcos2xdx 91 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions xdx Evaluate: ∫ 92 √1 + x2+√(1 + x2)3 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 2x + 1 Evaluate: ∫ dx 93 x4+ 2x3+ x2− 1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ dx 94 x2− x + 1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ dx 95 2x2+ x − 1 Watch Free Video Solution on Doubtnut

CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions cosx Evaluate: ∫ dx 96 sin(x − )sin(x + ) π π 6 6 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions sinx Evaluate: ∫ dx. 97 sin3x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ dx 98 3 + sin2x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ dx 99 1 + sinx + cosx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 3sinx + 2cosx Evaluate: ∫ dx 100 3cosx + 2sinx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions x2+ 1 Evaluate: ∫ dx 101 x4+ 1 Watch Free Video Solution on Doubtnut

CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions x2+ 4 Evaluate: ∫ dx 102 x4+ 16 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫√tanθdthη 103 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions x2− 1 Evaluate: ∫ 104 (x2+ 1)√1 + x4 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ dx 105 2x2+ x − 1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions x Evaluate: ∫ dx 106 x4+ x2+ 1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions

x2− 1 Evaluate: ∫ 107 dx 1 (x4+ 3x2+ 1)tan−1(x + ) x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ dx 108 x4+ 1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ dx 109 sin4x + cos4x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ dx 110 x2√1 + x2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions dx Evaluate: ∫ 111 3 (a2+ x2) 2 Watch Free Video Solution on Doubtnut

CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: ∫ dx 112 √(x − 1)(x − 2) Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions sec2x Evaluate: ∫ dx 113 √tan2x + 4 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions The number of irrational roots of the equation 4x 5x 3 is c. d. 1 114 + = − a.4 b. 0 2 x2+ x + 3 x2− 5x + 3 2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions

ex 115 Evaluate: ∫ dx e2x+ 6ex+ 5 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 4x + 1 Evaluate: ∫ 116 x2+ 3x + 2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 + x Evaluate: ∫√ dx. 117 x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions x2 Evaluate: ∫ dx 118 √1 − x6 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions x Evaluate: ∫√ dx 119 a3− x3 Watch Free Video Solution on Doubtnut

CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 1 Evaluate: 120 dx √1 − e2x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 2x + 3 Evaluate: ∫ dx 121 √x2+ 4x + 1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions 5 x 2 Evaluate: ∫ dx 122 √1 + x7 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Substitutions Evaluate: ∫x3d(tan−1x) 123 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Parts Evaluate: ∫xsin3xdx. 124 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Parts Evaluate: ∫xlogxdx. 125 Watch Free Video Solution on Doubtnut

CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Parts Evaluate: ∫sin−1xdx. 126 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Parts x − sinx Evaluate: ∫ dx 127 1 − cosx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Parts Evaluate is polynomaial function of then the degree, prove that ∫f(x) ∫exf(x)dx = ex[f(x)f'(x) + fx= fx+ ...... 128 + ( − 1)nfn(x)] fn(x)dx +dnf where dxn Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Parts x Evaluate: ∫sin−1√ dx. 129 a + x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation cosx Evaluate: − logxsinx)dx. ∫( 130 x

Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation 1 ∫(log(logx) + )dx Evaluate: 131 (logx)2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation Evaluate: ∫ex(f(x) + f′(x))dx = exf(x) + C 132 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation 1 1 Evaluate: ∫ex( )dx. − 133 x2 x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation exx Evaluate: ∫ dx 134 (x + 1)2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation 1 − sinx Evaluate: ∫ex( )dx 135 1 − cosx

Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation Evaluate: ∫{sin(logx) + cos(logx)}dx 136 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation logx Evaluate: ∫ dx 137 (1 + logx)2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation ∫esin−1xdx. Evaluate: 138 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation Evaluate: ∫xsin2xdx 139 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation

140 Evaluate: if ∫f(x)dx = g(x),then∫f−1(x)dx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation Evaluate: if ∫g(x)dx = g(x), then∫g(x){f(x) + f′(x)}dx 141 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation Evaluate: ∫cos√xdx 142 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation xsin−1x Evaluate: ∫ dx 143 √1 − x2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation Evaluate: ∫tan−1√xdx 144 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation

145 x Evaluate: ∫cosxlog(tan )dx 2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation 2 logx − 1 ∫( ) Evalaute: dx 146 1 + (logx)2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation ex(2 − x2)dx Evaluate: ∫ 147 (1 − x)√1 − x2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation Evaluate: ∫ex(1 + tanx + tan2x)dx 148 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation Evaluate: ∫sin2(logx)dx 149 Watch Free Video Solution on Doubtnut

CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation Evaluate: ∫[f(x)gx− fxg(x)]dx 150 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integration By Cancellation 1 − x Evaluate: ∫tan−1√ dx 151 1 + x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions 2x − 1 Evaluate: ∫ dx 152 (x − 1)(x + 2)(x − 3) Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions 2x Evaluate: ∫ dx 153 (x2+ 1)(x2+ 2) Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions 1 Evaluate: ∫ dx 154 sinx − sin2x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions 1 − cosx Evaluate: ∫ 155 cosx(1 + cosx)dx Watch Free Video Solution on Doubtnut

CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions (x − 1)(x − 2)(x − 3) Evaluate: ∫ dx 156 (x − 4)(x − 5)(x − 6) Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions x2+ 1 Evaluate: ∫ dx 157 (x − 1)2(x + 3) Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions x Evaluate: ∫ dx 158 (x − 1)(x2+ 4) Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions sinx Evaluate: ∫ dx 159 sin4x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions logexe ⋅ loge2xe ⋅ loge3xe Evaluate: ∫ dx x 160 Watch Free Video Solution on Doubtnut

CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions 1 Evaluate: ∫ dx 161 (x2− 4)√x + 1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions x2+ 1 Evaluate: ∫ dx 162 x(x2− 1) Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions 1 Evaluate: ∫ dx 163 x4− 1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions If the product of positive numbers is n . Then their sum is nn 164 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions dx Evaluate: ∫ 165 sinx(3 + cos2x) Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa By Partial Functions

cos2xsin4xdx Evaluate: ∫ 166 cos4x(1 + cos22x) Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 167 Evaluate: ∫√x2+ 2x + 5dx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 168 Evaluate: ∫√1 + 3x − x2dx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 169 Evaluate: ∫(x − 5)√x2+ xdx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 1 Evaluate: ∫ 170 (x − 3)√x + 1dx Watch Free Video Solution on Doubtnut

CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 1 Evaluate: ∫ 171 dx (x + 1)√x2− 1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 1 Evaluate: ∫ 172 dx (1 − x2)√1 + x2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 1 Evaluate: ∫ 173 dx (x + 1)√x2− 1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational Evaluate: ∫sec3xdx 174 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational + 1

x + 1 175 Evaluate: ∫ dx (x − 1)√x + 2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational x Evaluate: ∫ 176 dx (x2+ 4)√x2+ 1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 1 Evaluate: ∫ 177 dx (x + 1)√x2+ x + 1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational x3+ 1 178 Evaluate: ∫ dx x2+ x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 1 −dx 2 179 Evaluate: Evaluate: ∫x−11(1 + x4) Watch Free Video Solution on Doubtnut

CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 1 (x − x3) 3 180 Evaluate: ∫ dx x4 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 1 Evaluate: ∫ dx 181 1 [(x − 1)3(x + 2)5] 4 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational √tanx 182 Evaluate: ∫ dx sinxcosx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational dx Evaluate: ∫ 183 3√sin11xcosx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational sinx 184 Evaluate: ∫ dx 2 + sin2x Watch Free Video Solution on Doubtnut

CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational dx Evaluate: ∫ 185 4 x2(1 + x5) 5 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 1 Evaluate: ∫ 186 dx 3 x2(x4+ 1) 4 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 1 ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ (x4− x) 4 187 Evaluate: ∫ dx x5 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational x + 1 Evaluate: ∫ 188 dx (x − 1)√x + 2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational

189 Evaluate: ∫xx1n(ex)dx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational dx Evaluate: ∫ (x − p)√(x − p)(x − q) 190 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational n [√1 + x2+ x] 191 Evaluate: ∫ dx √1 + x2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational dx Evaluate: ∫ 192 cos3x√sin2x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Integrationa Functions Of Irrational 193

Evaluate: ∫sec5xcosec3xdx Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration b Evaluate: using limit of sum exdx ∫ 194 a Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration b Evaluate: using limit of sum sinxdx ∫ 195 a Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 2 Evaluate the definite integrals as limit of sums x2dx ∫ 196 1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration b dx Evaluate ∫ ,wherea,b > 0. 197 √x a Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1 1 1

198 1 1 1 Evaluate lim n→ ∞n[ ] + + + 6n2 (n + 1)(n + 2) (n + 2)(n + 4) Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1 1 1 1 Evaluate: lim n→ ∞[ ] + + + + 199 na + 1 na + 2 na nb Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1 ((n + 1)(n + 2)...(n + n)) n Evaluate: 200 lim n→ ∞ n Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration (12+ 22+ 33+ + n2)(13+ 23+ 33+ + n3) Evaluate: (lim)n− → 201 ∞ 16+ 26+ 36+ + n6 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration b Evaluate: ∫ cosxdx 202 a Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration b Evaluate: x3dx ∫ 203 a Watch Free Video Solution on Doubtnut

CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1 1 1 ∞( ) Evaluate: (lim)n− → + + + 204 √4n2− 1 √4n2− 22 √3n2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration sec21 sec24 1 1 Evaluate: + 2/n2 sec21] ∞[ (lim)n− → + + 205 n2 n2 n2 n Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration n k Evaluate ∑ (lim)n− → 206 ∞ n2+ k2 k=1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1 ∑r = 1n√r∑r = 1n √r Evaluate: 207 (lim)n− → ∞ ∑r = 1nr Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1/n n! Evaluate: (lim)n→ ∞[ ] 208 nn Watch Free Video Solution on Doubtnut

CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 0 dx Evaluate: ∫ 209 x2+ 2x + 2 −1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1 1 If then find the value of f(x) = min (|x|,1 − |x|, )∀x ∈ R, ∫ f(x)dx. 210 4 − 1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration π dx Find the mistake of the following evaluation of the integral I = ∫ 1 + 2sin2x 0 π dx I = ∫ 211 cos2x + 3sin2x sec2xdx 0 π 1 [tan−1(√3tanx)]π0 = 0 = ∫ = 1 + 3tan2x √3 0 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration tan−11 1 d Find the value of ( )dx ∫ 212 dx x −1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration Let be a continuous function on f Prove that there exists a number [a,b]. x ∈ [a, b]

213 x b such that ∫ f(t)dx = ∫ f(t)dt. a x Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1 e−xdx If , then find the value of k. ∫ = (log)e(1 + e) + k 214 1 + ex 0 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration A continuous real function satisfies f 1 2 . f(2x) = 3(f(x)∀x ∈ R 215 then find the value of If∫ ∫ f(x)dx = 1, f(x)dx 0 1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1 F ∈ dthevalueof∫ logxdx. 216 0 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1

1 217 If ,then find the value of xf' '(2x)dx f(0) = 1,f(2) = 3,f′(2) = 5 ∫ 0 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 2π dx x Consider the integral making the substitution we ∫ tan( ) = t, 5 − 2cosx 2 0 2π 0 2dt dx have The result is I = ∫ = ∫ = 0 218 5 − 2cosx 1−t2 (1 + t2)[5 − 2 ] 0 0 1+t2 obviously wrong, since the integrand is positive and consequently the integral of this function cannot be equal to zero. Find the mistake. Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration π dx Evaluate: ∫ 219 1 + sinx 0 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration ∞ −1dx Evaluate: (ex+1+ e3−x) ∫ 220 1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1 sin−1x √2 Evaluate: ∫ dx 221 (1 − x2)√1 − x2 0 Watch Free Video Solution on Doubtnut

CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 1 2 − x2 Evaluate: ∫ dx 222 (1 + x)√1 − x2 0 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration π dx 2 Evaluate: ∫ 223 a2cos2x + b2sin2x 0 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration π 2 Let: Then find the value of (1 − sint)nsin2tdt an= ∫ lim n→ ∞nan 224 0 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Definite Integration 102 1 1 (x − 1)(x − 2). .(x − 100) × ( ∫ + + x − 1 x − 2 0 225 .1 )dx = 101! − 100! . x − 100 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 2 Evaluate: ∣∣x3− x∣∣dx. ∫ 226 −1

Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 2π Evaluate: sin− 1(sinx)dx ∫ 227 π − 2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 1 1 Evaluate: sin−1(2x√1 − x2)dx. ∫ 228 √1 − x2 0 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals π 2 Evaluate: √cosx − cos3xdx ∫ 229 π − 2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals b |x| Show that ∫ dx = |b| − |a|. 230 x a Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals x Let: Then discuss continuity and differentiability of |2t − 3|dt. f(x) = ∫ 0 3

231 f(x)atx =3 2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals If denotes the greatest integer less than or equal to 2 x2[x]dx. then find the value of the [x] x, 232 integral ∫ 0 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 2 Evaluate: denotos the greatest integer function. [x2− x + 1]dx, where[.] ∫ 233 0 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 5π 12 Evaluate: , where denotes the greatest integer function. ∫ [tanx]dx [.] 234 0 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 10π Evaluate: represents greatest integer function. [tan−1x]dx,where[x] ∫ 235 0 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals ∞

∞ Evaluate: represents greatest integer function. [2e−x]dx, where[x] ∫ 236 0 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 2π Evaluate: ,where denotes the greatest integer function. [.] ∫ [sinx]dx 237 0 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 5 1 Evaluate: denotes the greatest integer function). x2[x + ]dx(where[.] ∫ 238 2 −5 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals π 2 Evaluate: ∫ |sinx − cosx|dx 239 0 Watch Free Video Solution on Doubtnut

CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 4 4 Evaluate: then find the value of ∫ f(x)dx = 4and∫ (3 − f(x))dx = 7, 240 −1 2 −1 ∫ f(x)dx. 2 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 3 x2+ 1 x Evaluate: (tan−1( ) + tan−1( ))dx ∫ 241 x2+ 1 x −1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals a .a− [ (log)ax]dx,(a > 1). Evaluate: ∫ x 242 1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals e6 logx Evaluate: denotes the greatest integer function. ]dx,where[.] [ ∫ 243 3 1 Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 1 Find the value of denote the greatest function [x2+ {x}]dx, where[.]and{.} ∫ 244 −1 and fractional parts of respectively. x, Watch Free Video Solution on Doubtnut CENGAGE_MATHS_CALCULUS_INTEGRALS_Properties Of Definite Integrals 2π Evaluate: , where denotes the greatest integer function [cot−1]dx ∫ [.] 245 π 2 Watch Free Video Solution on Doubtnut

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## Class 12 Maths

NCERT Solutions covers all exercise questions given in the CBSE textbook. ... Our best Class 12 Maths master teachers have reviewed all the class 12 Mathematics NCERT Solutions of exercise questions that will help you solve all the NCERT. For more help visit my site:- https://www.extramarks.com/ncert-solutions/cbse-class-12/mathematics

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## CBSE Class 12 Maths Syllabus

We offered the best Solutions for CBSE Class 12 Maths Syllabus has been written to help students like you who are appearing for different board exams as well as the JEE. Student Easley understanding of all important concepts covered in each chapter. More info:-https://www.extramarks.com/syllabus/cbse-class-12

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## Class 11 Maths Ncert Solutions

Are you looking for the most accurate Class 11 Maths Ncert Solutions, then Extramarks is the perfect website to download it in PDF format for fully free. Visit our site:- https://www.extramarks.com/ncert-solutions/cbse-class-11/mathematics

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## Class 12 Maths NCERT Solutions Available Here

Extramarks Education is a website that offers learners the opportunity to improve their educational effectiveness. The firm has a number of apps which affect student achievement significantly. The Extramarks Learning App offers assistance to students of all classes, for both ICSE and CBSE boards. Download the app now and reduce school stress. Click on the link provided for class 12 Maths NCERT solutions.

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## Maths solutions Class 9 on Extramarks

Are you looking for detailed explanations or solutions to the chapter in NCERT, Linear Equation in Two Variables for Class 9 Maths? Consider your search officially over because you can now get access to all the study materials that you can possibly need to ace your Maths exam, only on the Extramarks app or website. To know more, download the Extramarks learning app right away.

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## Maths Learning Solutions for ICSE Class 8

ICSE 8th Class Maths can be made easier by the Extramarks app. The app has many interactive learning solutions that can make the students learn in a better way and become better learners. The app is a reliable source of learning as the content on the app is curated by experts and every topic is explained in great detail that can speed up the learning process.

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## Check Out The Website for CBSE Class 12 Maths Sample Paper Solutions

CBSE Class 12 Maths Sample Paper Solutions are easy to navigate and access on Extramarks website. Extramarks supports you with techniques of learning and gasping all the study material effectively in simple ways with the help of interactive learning tools. The previous year question papers are essential for the students to understand the different types of questions that can appear in the exams and the pattern as they are prepared on the basis of previous exams. Browse through the one-stop solution for all the academic needs of the students.

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## Ncert Solutions for Class 7 Maths Chapter 12

This chapter is a continuation of the already studied algebra chapters in the previous classes. In this chapter, you will learn more about algebraic expressions. You will understand the formation of an expression, terms of expression and operations on the expressions. In this chapter, you will learn to solve problems on algebraic expressions to find any unknown value using the expressions. You will also learn about the different types of expressions depending on the number of terms. https://www.urbanpro.com/ncert-solutions/class-7/maths-algebraic-expressions

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## NCERT solutions for class 12 Maths

NCERT Solutions for class 12 Maths: Students are preparing for the board exam in class 12. This year is considered as the year of career where there is huge opportunity lined up based on their performance. Class 12 maths are crucial during the preparation of board exam. Therefore, NCERT solutions for class 12 is prepared for the student to practice any difficult questions. Syllabus for maths is shared in this article along with the solutions. NCERT solutions are even useful for preparation of competitive engineering exams. CBSE NCERT solutions help students in securing good CGPA. You can download the NCERT solutions and practice for the exams.

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## NCERT Solutions For Class 10 Maths | Entrancei

Entrancei is the one number online resource portal in India with the vision to reach and assist the students in their exam preparation and much more. Entrancei mathematics expert educator made up NCERT Solutions for Class 10 Maths, you can get easily download and share with your classmate and friends. You can get easily with one click http://entancei.over-blog.com/2020/05/ncert-solutions-for-class-10-maths-entrancei.html

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## ncert solutions for class 7 maths

Class 10 is an important time for students on their study trip. In addition, grades earned on the tenth-grade exam will also help students choose the desired flow for higher education. Therefore, it is important that all students study effectively and score well on the CBSE Class 10 Board Exam.

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## NCERT Solutions for Class 8 Maths - Fliplearn

Searching for the best comprehensive, exact and free pdf of NCERT Solutions for Class 8 Maths? Look no further, your inquiry currently finishes here! Our best Maths master teachers have surveyed and talked out point by point chapter insightful NCERT Solutions for Class 8 Maths. The Maths NCERT Solutions Class 8 explained in this presentation will assist you with comprehension and tackle all the class 8 mathematics book questions. The exercise solutions accessible at Fliplearn are free and accessible in PDF format. https://cutt.ly/7s4tZYE

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## Worksheets for Class 12 Integrals

Download KVS CBSE NCERT Class 12 Integrals Worksheets in pdf free for all chapters with solutions as per latest 2020 2021 textbooks and syllabus https://www.studiestoday.com/worksheets/477/integrals.html

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## ncert class 8 maths solutions pdf download

Are you looking for comprehensive study guides to ace your Class 8 exams? Look no further! Our collection of study guides is specifically designed to provide you with the necessary tools and resources for effective exam preparation. Covering all subjects and topics included in the Class 8 curriculum, our study guides offer in-depth explanations, practice questions, and valuable tips to enhance your understanding and boost your confidence. With our comprehensive study guides by your side, you'll be well-equipped to excel in your exams and achieve academic success in Class 8.

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## Ncert Solutions For Class 12

NCERT Solutions for Class 12 provide a comprehensive and enriching learning journey. With a focus on conceptual clarity and academic excellence, these solutions undoubtedly play a pivotal role in nurturing confident and knowledgeable individuals.

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