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CBSE Questions for Class 12 Commerce Applied Mathematics Indefinite Integrals Quiz 1 - MCQExams.com

10tan1xdx.
  • π212log2.
  • π4+12log2.
  • π214log2.
  • π412log2.
dxx10x2;x>1= ______ +C.
  • 14log|x10x2+x2|
  • 12log|x10x2|
  • 14sec1(x4)
  • 14sec1(x4)
The value of logxdx is
  • xlog(xe)+c
  • x2logx+c
  • exlogx+c
  • (x+1)logx+c
x.exdx=
  • x.ex+c
  • ex(x1)+c
  • ex(x+1)+c
  • ex(x+2)+c
x3exdx=
  • ex(x33x2+6x+6)+c
  • ex(x33x2+6x6)+c
  • ex(x3+3x2+6x+6)+c
  • ex(x33x26x+6)+c
logx+1dx=
  • 12[(x+1)log(x+1)x]+c
  • 12[(x1)log(x+1)x]+c
  • 12[xlog(x+1)x22]+c
  • 12[(x+1)log(x+1)x2]+c
[sin(logx)+cos(logx)]dx=
  • exsin(logx)+c
  • excos(logx)+c
  • xsin(logx)+c
  • xcos(logx)+c
The integral (1+x1x)ex+1xdx is equal to 
  • (x1)ex+1x+c
  • xex+1x+c
  • (x+1)ex+1x+c
  • xex+1x+c
The integral xcos1(1x21+x2)dx is equal to :
(Note : (x>0))
  • x+(1+x2)cot1x+c
  • x+(1+x2)tan1x+c
  • x(1+x2)tan1xc
  • x(1+x2)cot1x+c
If f(x) dx =Ψ(x) , then x5f(x3) dx is equal to
  • 13x3Ψ(x3)3x3Ψ(x3)dx+C
  • 13x3Ψ(x3)x2Ψ(x3)dx+C
  • 13[x3Ψ(x3)x3Ψ(x3)dx]+C
  • 13[x3Ψ(x3)x2Ψ(x3)dx]+C
If f and g(x)=f'(x) and \displaystyle{F}({x})=\left ({f}\left (\frac{{x}}{2}\right)\right)^{2}+\left ({g}\left (\frac{{x}}{2}\right)\right)^{2} and given that F(5)=5, then F(10) is equal to 
  • 5
  • 10
  • 0
  • 15
\int \frac{ f(x) g'(x)-f'(x)g(x)}{f(x)g(x)}\begin{bmatrix} Log (g(x))-Log (f(x)) \end{bmatrix}dx=
  • Log\begin{pmatrix} \frac {g(x)}{f(x)}\end{pmatrix}+C
  • \frac {1 }{2 } \begin {vmatrix} Log \begin{pmatrix} \frac {g(x)}{f(x)}\end{pmatrix} \end {vmatrix}^2+C
  • \dfrac {(g)x}{f(x)}Log \begin {pmatrix}\frac {g(x)}{f(x)}\end {pmatrix} +C
  • Log\begin{bmatrix} \frac {g(x)}{f(x)} \end{bmatrix}-\frac {g(x)}{f(x)}+C
\int x  log  x  dx is equal to
  • \displaystyle\frac{x^2}{4}(2log x-1)+c
  • \displaystyle\frac{x^2}{2}(2log x-1)+c
  • \displaystyle\frac{x^2}{4}(2log x+1)+c
  • \displaystyle\frac{x^2}{2}(2log x+1)
The value of \int { { e }^{ \tan { \theta  }  } } \left( \sec { \theta  } -\sin { \theta  }  \right) d\theta is equal to ?
  • -{ e }^{ \tan { \theta } }\sin { \theta } +C
  • { e }^{ \tan { \theta } }\sin { \theta } +C
  • { e }^{ \tan { \theta } }\sec { \theta } +C
  • { e }^{ \tan { \theta } }\cos { \theta } +C
\displaystyle \int { \log { \left( \log { x }  \right) +\dfrac { 1 }{ \log { x }  }  }  } dx
  • x\log { \left( \log { x } \right) +c }
  • x\log { x } +c
  • x+c
  • None
The integral of \displaystyle\int e^{x} (\sin x+\cos x)dx is
  • e^{ x} \cos x + c
  • e^{x}\sin x + c
  • e^{ x}\sec x + c
  • none of this
If \displaystyle\int { \frac { { 2 }^{ x } }{ \sqrt { 1-{ 4 }^{ x } }  }  } dx=K\sin ^{ -1 }{ \left( { 2 }^{ x } \right)  } +C, then the value of K is equal to
  • \ell n\ 2
  • \dfrac {1}{2} \ell n\ 2
  • \dfrac {1}{2}
  • \dfrac {1}{\ell n\ 2}
The value of integral \int {{{\tan }^{ - 1}}\left( {\dfrac{{{x^3}}}{{1 + {x^2}}}} \right)}  + {\tan ^{ - 1}}\left({\dfrac{{1 + {x^2}}}{{{x^3}}}} \right)dx is equal to 
  • 1
  • - \dfrac{\pi }{2} + c
  • \dfrac{\pi }{2} + c
  • \left( {\dfrac{\pi }{2}} \right)x + c

\int ( e^{\log x} + \sin x) \cos x \  dx is equal to

  • x \sin x + \cos x - \dfrac {\sin^2x}{2}+ c
  • x \cos x - \sin^2x+ c
  • x \sin x + \cos x - (\cos^2x)/2+ c
  • x^2 \sin^x + \cos x - \sin^3 x + c
\int_{}^{} {x{{\sin }^{ - 1}}xdx}
  • \frac{1}{4}{\sin ^{ - 1}}x\left( {2x + 1} \right) + \frac{{x\sqrt {1 - {x^2}} }}{4} + c
  • \frac{1}{4}{\sin ^{ - 1}}x\left( {2{x^2} + 1} \right) + \frac{{x\sqrt {1 - {x^2}} }}{4} + c]
  • \frac{1}{4}{\cos ^{ - 1}}x\left( {2x + 1} \right) + \frac{{x\sqrt {1 - {x^2}} }}{4} + c
  • \frac{1}{4}{\sin ^{ - 1}}x\left( {2x + 1} \right) - \frac{{x\sqrt {1 - {x^2}} }}{4} + c
Solve \int {\dfrac{1}{{\sqrt[{}]{{9 - 25{x^2}}}}}} dx
  • \dfrac{1}{5}{{\sin }^{-1}}\left( \dfrac{5x}{3} \right)+C
  • {{\sin }^{-1}}\left( \dfrac{5x}{3} \right)+C
  • \dfrac{1}{5}{{\sin }^{-1}}\left( \dfrac{3x}{5} \right)+C
  • {{\sin }^{-1}}\left( \dfrac{3x}{5} \right)+C
Find the general solution of \frac{{dy}}{{dx}} = \frac{{2y}}{x}
  • y=e^{5\log x +c}
  • y=e^{3\log x +c}
  • y=e^{2\log x +c}
  • None of these
The value of \int _{  }^{  }{ \cfrac { \log { x }  }{ { \left( x+1 \right)  }^{ 2 } }  } dx is
  • \cfrac { -\log { x } }{ x+1 } +\log { x } -\log { \left( x+1 \right) } +C
  • \cfrac { \log { x } }{ x+1 } +\log { x } -\log { \left( x+1 \right) } +C 
  • \cfrac { \log { x } }{ x+1 } -\log { x } -\log { \left( x+1 \right) } + C
  • \cfrac { -\log { x } }{ x+1 } -\log { x } -\log { \left( x+1 \right) } +C 
\displaystyle \int \sin x \log (\sec x+\tan x)dx=f(x)+x+c then f(x)=
  • \cos x \log(\sec x + \tan x)+c
  • \sin x\log(\sec x+\tan x)+c
  • - \cos x \log\sec x+\tan x)+c
  • -\cos x\log \sec x+c
\int [\frac{f(x)g'(x)-f'(x)g(x)}{f(x)g(x)}].[log (g(x))-log(f(x))]dx=
  • log\frac{g(x)}{f(x)}+c
  • \frac{1}{2}(log\frac{g(x)}{f(x)})^{2}+c
  • \frac{g(x)}{f(x)}log(\frac{g(x)}{f(x)})+c
  • \frac{f(x)}{g(x)}log(\frac{g(x)}{f(x)})+c
\frac{1}{2}\int \sqrt{x^{3}-8x^{2}dx} equals
  • {\frac{(x-8)^{5/2}}{5}+\frac{8(x-8)^{3/2}}{3}}+c
  • {\frac{(x-8)^{5/2}}{5}+\frac{8}{3}(x-8)^{3/2}}+c
  • {\frac{(x-8)^{5/2}}{3}+\frac{8}{5}(x-8)^{3/2}}+c
  • None of these
\int\ \sec\theta\ d\theta
  • \dfrac{(\sec\theta+\tan\theta)}{2}+c
  • \dfrac{(\sec\theta+\tan\theta)}{3}[2+4\tan\theta(\sec\theta+\tan\theta)]+c
  • \ln {(|\sec\theta+\tan\theta|)}+c
  • \dfrac{3(\sec\theta+\tan\theta)}{2}[2+\tan\theta(\sec\theta+\tan\theta)]+c
\int {\dfrac{{\cot \sqrt x }}{{2\sqrt x }}dx} is equal to = \_\_\_\_\_ + C.
  • 2\log |\sin \sqrt x |
  • \log |\sin \sqrt x |
  • \dfrac{1}{2}\log |\sin \sqrt x |
  • None of these
Evaluate :
\int \cos^3 x e^{\log \sin x} dx
  • -\dfrac{\cos ^4x}{4}+C
  • \dfrac{\sin x}{x^2}+C
  • -\dfrac{\sin^3x}{3}+C
  • None of these
The value of \int { (x-1) } { e }^{ -x } dx is equal to 
  • -{ xe }^{ x }+C
  • { xe }^{ x }+C
  • -{ xe }^{ -x }+C
  • { xe }^{ -x }+C
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Practice Class 12 Commerce Applied Mathematics Quiz Questions and Answers