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CBSE Questions for Class 12 Commerce Maths Integrals Quiz 2 - MCQExams.com

The integral 10(tan1x)31+x2dx=
  • π464
  • π4256
  • π41024
  • π4512

The integral π/40etanxcos2xdx=
  • e1
  • e11
  • e1+1
  • e21

1/20ex[sin1x+11x2] dx =


  • e44
  • πe6
  • πe4
  • πe2
If  k0cosx1+sin2xdx=π4 then k=?
  • 1
  • π/4
  • π/2
  • π/6

10tanhxdx=
  • log(e+1/e)
  • log (e1/e)
  • log(e/2+1/2e)
  • log(e21e)
Evaluate the integral
e1(lnx)3xdx
  • e4/4
  • 14
  • 14(e41)
  • e41

π0tanxsecx+cosxdx=
  • π
  • π2
  • π
  • 2π
Evaluate: 158x1+x2.dx
  • 158
  • 373
  • 376
  • 379

10ex(ex+1)3dx=
  • e444
  • (e+1)444
  • (e+1)4+164
  • (e+1)44+4

10xdx(x2+1)2=
  • 1/2
  • 1/3
  • 1/4
  • 0
Evaluate: π20esin2xsin2xdx
  • e
  • e+1
  • e1
  • 2e+1

4016x2dX=
  • π4
  • π
  • 16π
  • 4π

Find π20sec2xdx(secx+tanx)n, where (n>2)
  • 1n21
  • nn21
  • nn2+1
  • 2n21
π/20dX4cos2x+9sin2x=
  • π12
  • π4
  • π9
  • π6
Evaluate the following definite integral:
π/2014+5cosxdx=
  • 15log2
  • 12log2
  • 13log3
  • 13log2
1012+3xdx=
  • 23(52)
  • 23(5+2)
  • 35(52)
  • 23(32)

0(axbx)dx=(a>1,b>1)
  • 1loga1logb
  • logalogb
  • loga+logb
  • 1loga+1logb

a0xax+adx=
  • a+2alog2
  • a2alog2
  • 2aloga
  • 2alog2

If 600dx2x+1=loga, then a=
  • 3
  • 11
  • 81
  • 40
Evaluate the integral
101x1+xdx
  • log4
  • log(4e)
  • 1
  • log(e4)

21dx1+x2=
  • loge(2+52+1)
  • loge(2+12+5)
  • loge(2521)
  • 0
11dx1+x2=
  • 0
  • π2
  • π4
  • π6
Evaluate the integral
21(x1)(2x)dx
  • π8
  • π4
  • 18
  • 14

1(11+x2)dx=

  • π4
  • π4
  • π2
  • π2
Evaluate: π/80cos34x dx
  • 1/6
  • 1/5
  • 1/3
  • 1/8
sec2x.cosec2xdx=
  • tanxcotx+c
  • tanx+cotx+c
  • tanx+cotx+c
  • secxtanx+c
π/20sin4x.cos2xdX=
  • π32
  • π216
  • π15
  • π64
Evaluate the integral
31dX(x1)(3x)
  • π
  • π
  • π/2
  • 0

\displaystyle \int_{0}^{\infty}\frac{dx}{(x+\sqrt{x^{2}+1})^{5}}=
  • 1/24
  • 1/5
  • 5/24
  • 5/36
Evaluate : \displaystyle \int\frac{\cot^{2}x}{(co\sec^{2}x+co\sec x)}d{x}
  • x-\sin x +C
  • x + \cos x +C
  • \sin x - x+C 
  • 2\tan(\displaystyle \frac{ax}{2})+c
\displaystyle \int_{0}^{1}\sqrt{x(1-x)}dx=
  • \pi /2
  • \pi /4
  • \pi /6
  • \pi /8
Evaluate the integral
\displaystyle\int_{\pi}^{5\pi/4}\frac{\sin 2x}{\cos^4 x + \sin^4 x}dx
  • \displaystyle \frac{5\pi}{4}
  • \displaystyle \frac{\pi}{2}
  • \pi
  • \displaystyle \frac{\pi}{4}

\displaystyle \int_{0}^{a}\frac{x^{5}dx}{\sqrt{a^{2}-x^{2}}}=
  • \displaystyle \frac{\mathrm{a}^{5}}{15}
  • \displaystyle \frac{8\mathrm{a}^{5}}{15}
  • \displaystyle \frac{8a}{15}
  • \displaystyle \frac{11\mathrm{a}^{2}}{15}
Evaluate the integral
\displaystyle \int_{0}^{1}  cos ^{-1}\left(\displaystyle \frac{1- {x}^{2}}{1+ {x}^{2}}\right) {d} {x}
  • \displaystyle \frac{\pi}{2} -\log 2
  • \displaystyle \frac{\pi}{2}+\log 2
  • \displaystyle \frac{\pi}{4} - log 2
  • \displaystyle \frac{\pi}{4} - log 3
Evaluate: \displaystyle \int_{1/3}^{1}\frac{(x-x^{3})^{1/3}}{x^{4}}dx.
  • 3
  • 0
  • 6
  • 4

\displaystyle \int_{\log 2}^{t}\frac{d_{X}}{\sqrt{e^{x}-1}}=\frac{\pi}{6}, then \mathrm{t}=
  • 4
  • \log 8
  • log 4
  • log 2
Evaluate: \displaystyle \int_{0}^{\pi /2} \sin^{3}x.\cos^{3}x dx
  • \displaystyle \frac{1}{12}
  • \displaystyle \frac{\pi}{24}
  • \displaystyle \frac{\pi}{12}
  • \displaystyle \frac{1}{24}
Evaluate: \displaystyle \int_{0}^{1} \cos \left(2 \cot^{-1}\sqrt{\displaystyle \frac{1- {x}}{1+ {x}}}\right)dx
  • \dfrac{-1}{2}
  • \dfrac{1}{2}
  • 0
  • 1
Evaluate the integral
I=\displaystyle \int _{ 0 }^{ \frac { 1 }{ \sqrt { 2 }  }  }{ \cfrac { { sin }^{ -1 }x }{ { \left( 1-{ x }^{ 2 } \right)  }^{ \frac { 3 }{ 2 }  } } dx }  
  • \displaystyle \frac{\pi}{4}+\frac{1}{2} log 2
  • \displaystyle \frac{\pi}{4}-\frac{1}{2} log 2
  • \displaystyle \frac{\pi}{3}
  • \displaystyle \frac{\pi}{6}

lf 0<\mathrm{a}<\mathrm{c},\ 0<\mathrm{b}<\mathrm{c} then \displaystyle \int_{0}^{\infty}\frac{a^{x}-b^{x}}{c^{x}}dx=
  • \displaystyle \log\frac{b}{c}-\log\frac{a}{c}
  • \displaystyle \frac{\log a-\log b}{\log c}
  • \displaystyle \frac{1}{\log b/c}-\frac{1}{\log a/c}
  • l\displaystyle \mathrm{o}\mathrm{g}\frac{\mathrm{a}}{\mathrm{c}}-l\mathrm{o}\mathrm{g}\frac{\mathrm{b}}{\mathrm{c}}

\displaystyle \int_{0}^{1}\frac{xe^{x}}{(x+1)^{2}}dx=
  • \displaystyle \frac{e}{2}
  • \displaystyle \frac{e-1}{2}
  • \displaystyle \frac{e}{2}-1
  • \displaystyle \frac{e-3}{2}

The solution of the equation \displaystyle \int_{\sqrt{2}}^{\mathrm{x}}\frac{\mathrm{d}\mathrm{x}}{\mathrm{x}\sqrt{\mathrm{x}^{2}-1}}=\frac{\pi}{12} is
  • 1
  • 1/2
  • 2
  • -2
Evaluate the integral
\displaystyle \int_{0}^{1}\frac{ {d} {x}}{ {x}^{2}+2 {x} {c} {o} {s}\alpha+1}
  • \sin \alpha
  • \tan^{-1} (\sin \alpha)
  • \dfrac{\alpha}{(2\sin \alpha)}
  • \alpha (\sin \alpha)

\displaystyle \int_{0}^{\pi/2}\frac{1}{1+4\sin^{2}x}dx=
  • \displaystyle \frac{\pi}{\sqrt{5}}
  • \displaystyle \frac{\pi}{2\sqrt{5}}
  • \displaystyle \frac{\pi}{2}
  • \displaystyle \frac{\pi}{3\sqrt{5}}

\displaystyle \int_{0}^{16}\frac{dx}{\sqrt{x+9}-\sqrt{x}}=
  • 10
  • 12
  • 14
  • 16

\displaystyle \int_{0}^{1}\frac{\sqrt{x}}{1+x}dx_{=}
  • 2-\pi/2
  • 1-\pi/2
  • \pi/2
  • 2+\pi/2

\displaystyle \int_{0}^{\pi/4}\frac{\sqrt{\tan x}}{sin x cos x}dx=
  • 1
  • 2
  • 0
  • 4

\displaystyle \int_{1}^{2}\frac{dx}{x^{2}-2x+4}=
  • 0
  • \displaystyle \frac{\pi}{2}
  • \displaystyle \frac{\pi}{3}
  • \displaystyle \frac{\pi}{6\sqrt{3}}

\displaystyle \int_{0}^{1}\frac{x}{1+\sqrt{x}}dx_{=}
  • \frac{5}{3}-\log 4
  • \frac{5}{3}+\log 4
  • \frac{5}{3}\log 4
  • \displaystyle \frac{3}{5}-l\mathrm{o}\mathrm{g}4\frac{3}{5}-l\mathrm{o}\mathrm{g}4

\displaystyle \int_{0}^{\pi}\frac{dx}{3+2\sin x+\cos x}=
  • \pi/3
  • \pi/4
  • \pi/6
  • \pi/2
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