Loading [MathJax]/jax/element/mml/optable/GeneralPunctuation.js

CBSE Questions for Class 12 Commerce Applied Mathematics Indefinite Integrals Quiz 11 - MCQExams.com

Evaluate : cotx(cosecxcotx)dx
  • cosecxcotxx+C
  • cosecxcotxx+C
  • cosecx+cotxx+C
  • sinx+x+C
Let x1/21x3dx=23gof(x)+c then
  • f(x)=x
  • f(x)=x3/2
  • f(x)=x2/3
  • g(x)=sin1x
xex(1+x)2dx is equal to
  • exx+1+c
  • ex(x+1)+c
  • ex(x+1)+c
  • ex1+x2+c
Evaluate : (cos2xcos2α)(cosxcosα)dx
  • 2sinx+xcosα+C
  • 2sinx2xcosα+C
  • 2sinx+2xcosα+C
  • 2sinx2xcosα+C
Evaluate : (1sinx)cos2xdx
  • tanx+secx+C
  • tanxsecx+C
  • tanx+secx+C
  • tanxsecx+C
The value of e11+x2lnxx+x2lnxdx is
  • e
  • ln(1+e)
  • e+ln(1+e)
  • eln(1+e)
If 21ex2dx=a, then e4elnxdx is equal to
  • 2e42ea
  • 2e4ea
  • 2e4e2a
  • e4ea
The value of ex(2x2)(1x)1x2dx is equal to
  • ex1+x1x+c
  • ex1+x+c
  • ex1x+c
  • ex1x1+x+c
Evaluate 3xcos4xdx=
  • 3x(log3)2+16[(log3)cos4x+4sin4x]+c
  • 3x9+(log4)2[cos4x+(log3)sin4x]+c
  • 3x(log3)2+(log4)2[(log3)sin4x+(log4)cos3x]+c
  • 3x(log3)2+16[(log3)sin4x+(log4)cos3x]+c
logx2008(logx+1)2010dx=
  • 1(logx+1)2008+c
  • x(logx+1)2010+c
  • 1(logx+1)2009+c
  • x(logx+1)2009+c
Let f be a function defined for every x, such that f'' = -f ,f(0)=0, f' (0) = 1, then f(x) is equal to
  • tanx
  • ex1
  • sinx
  • 2sinx
\displaystyle \int\frac{\sin^{-1}x-\cos^{-1}x}{\sin^{-1}x+\cos^{-1}x}dx=
  • \displaystyle \frac{4}{\pi}[x\sin^{-1}x+\sqrt{1-x^{2}}]-x+c
  • \log[\sin^{-1}x+\cos^{-1}x]+c
  • \dfrac{4}{\pi}[x\sin^{-1}x+\sqrt{1-x^{2}}]+c
  • \dfrac{4}{\pi}[x\sin^{-1}x-\sqrt{1-x^{2}}]+C
If \displaystyle\int xe^{-5x^{2}}\sin4x^{2}dx=e^{-5x^{2}} (A \sin4x^{2}+B\cos4x^{2})+C, then A+B
  • -\dfrac{1}{66}
  • \dfrac{1}{66}
  • -\dfrac{9}{66}
  • -\dfrac{7}{66}
\displaystyle \int\frac{\cos x-1}{\sin x+1}e^{x}dx is equal to
  • \displaystyle \frac{e^{x}\cos x}{1+\sin x}+c
  • c-\displaystyle \frac{e^{x}\sin x}{1+\sin x}
  • c-\displaystyle \frac{e^{x}}{1+\sin x}
  • c-\displaystyle \frac{e^{x}cosx}{1+\sin x}
\displaystyle \int(\frac{x+2}{x+4})^{2}e^{x}dx is equal to
  • e^{x}(\displaystyle \frac{x}{x+4})+c
  • e^{x}(\displaystyle \frac{x+2}{x+4})+c
  • e^{x}(\displaystyle \frac{x-2}{x+4})+c
  • (\displaystyle \frac{2xe^{x}}{x+4})+c
The value of \displaystyle \int(3x^{2}\tan\frac{1}{x}-x\sec^{2}\frac{1}{x})dx {\it} is
  • x^{3}\displaystyle \tan\frac{1}{x}+c
  • x^{2}\displaystyle \tan\frac{1}{x}+c
  • x\displaystyle \tan\frac{1}{x}+c
  • \displaystyle \tan\frac{1}{x}+c
\displaystyle \int e^{2x} (\sqrt{3}cosx-sinx)dx=
  • \displaystyle \frac{e^{2x}}{5}[(2\sqrt{3}+1)cosx -(\sqrt{3}-2)sinx]+c
  • \displaystyle \frac{e^{2x}}{5}[(2\sqrt{3}+1)sinx+(\sqrt{3}-2)\cos x]+c
  • \displaystyle \frac{e^{2x}}{5}[(2\sqrt{3}+1)sinx-(\sqrt{3}-2)cosx]+c
  • \displaystyle \frac{e^{2x}}{5}[(2\sqrt{3}+1)cosx+(\sqrt{3}-2)sin x]+c
If \displaystyle \int\frac{e^{4x}-1}{e^{2x}}\log(\frac{e^{2x}+1}{e^{2x}-1})ck=\frac{t^{2}}{2}\log t-\frac{t^{2}}{4}-\frac{u^{2}}{2} \log u + \frac{u^{2}}{4}+c then
  • \displaystyle t=e^{-x}-e^{x},u=e^{x}+e^{-x}
  • \displaystyle t=e^{x}-e^{-x},u=e^{x}+e^{-x}
  • \displaystyle t=e^{x}+e^{-x},u=e^{x}-e^{-x}
  • \displaystyle u=e^{-x}-e^{x},t=e^{x}+e^{-x}
\displaystyle \int \cos x\log(\tan \frac{x}{2})dx=
  • \displaystyle \sin x \log|\tan x|-x+c
  • \displaystyle -\sin x \log|\tan \frac{x}{2}|+x+c
  • \displaystyle -\sin x \log|\tan \frac{x}{2}|-x+c
  • \displaystyle \sin x \log|\tan \frac{x}{2}|-x+c
\displaystyle \int \cos^{-1}\sqrt{\frac{1-x}{2}}dx=
  • \displaystyle \frac{\pi}{2}x-\frac{1}{2}xcos^{-1}x+c
  • \dfrac{\pi}{2}x-\dfrac{1}{2}xcos^{-1}x+\dfrac{1}{2}\sqrt{1-x^{2}}+c
  • \dfrac{\pi}{2}x-\dfrac{1}{2}xcos^{-1}x-\sqrt{1-x^{2}}+c
  • \displaystyle \dfrac{\pi}{2}x+\dfrac{1}{2}xcos^{-1}x+c
\displaystyle \int x^{3}e^{x^{2}}dx=
  • \displaystyle \frac{1}{2}e^{x^{2}}(x^{2}-1)+c
  • e^{x^{2}}(x^{2}-1)+c
  • \dfrac{1}{2}e^{x^{2}}(x^{2}+1)+c
  • e^{x^{2}}(x^{2}+1)+c
\displaystyle \int\dfrac{e^{(x^{2}+4\ln x)}-x^{3}e^{x^{2}}}{x-1}dx is equal to
  • (\displaystyle \dfrac{e^{3\ln x}-e^{\ln x}}{2x})e^{x^{2}}+c
  • \displaystyle \dfrac{(x-1)xe^{x^{2}}}{2}+c
  • \displaystyle \dfrac{(x-1)xe^{x^{2}}}{2x}+c
  • \dfrac{1}{2}(x^{2}-1)e^{x^{2}}+c
lf f(x) is a polynomial of nth degree then \displaystyle \int e^{x}f(x)dx=
  • e^{x}[f(x)-f^{'}(x)+f^{''}(x)-f^{'''}(x)+\ldots\ldots+(-1)^{n}f^{n}(x)] Where f^{n}(x) denotes nth order derivative of w.r.t. x
  • e^{x}[f(x)+f(x)+f^{'}(x)+f^{''}(x)+\ldots\ldots+(-1)^{n}J^{n}(x)]
  • e^{x}[f(x)+f^{'}(x)+f^{'}(x)+f^{'''}(x)+\ldots\ldots+(-1)^{n}f^{2n}(x)]
  • d[f(x)+f(x)+f^{'}(x)+f^{'''}(x)+\ldots\ldots+\{-1)^{n}f^{3n}(x)]
\displaystyle \int_{0}^{\pi }\left \{ f(x) +f^{''}(x)\right \}\sin\, x\, dx=5,f(\pi )= Then f(0) equals 
  • 2
  • 3
  • 5
  • 4
\displaystyle \int \frac{\mathrm{cosec} ^{2}x-2005}{\cos ^{2005}x}dx is equal to
  • \displaystyle \frac{\cot x}{(\cos x)^{2005}}+c
  • \displaystyle \frac{\tan x}{(\cos x)^{2005}}+c
  • \displaystyle \frac{(-\tan x)}{(\cos x)^{2005}}+c
  • none of these
Evaluate: \displaystyle \int x\left ( \frac{\ln a^{a^{x/2}}}{3a^{5x/2}b^{3x}}+\frac{\ln b^{b^{x}}}{2a^{2x}b^{4x}} \right )
  • \displaystyle \frac{1}{6\ln a^{2}b^{3}}a^{2x}b^{3x}\ln \frac{a^{2x}b^{3x}}{e}+k
  • -\displaystyle \frac{1}{6\ln a^{2}b^{3}}\frac{1}{a^{2x}b^{3x}}\ln \frac{1}{ea^{2x}b^{3x}}+k
  • \displaystyle \frac{1}{6\ln a^{2}b^{3}}\frac{1}{a^{2x}b^{3x}}\ln (a^{2x}b^{3x})+k
  • \displaystyle \frac{1}{6\ln a^{2}b^{3}}\frac{1}{a^{2x}b^{3x}}\ln (a^{2x}b^{4x})+k
If \displaystyle I_{n}=\int (\ln x)^{n} dx, then I_{n}+nI_{n-1}=
  • \displaystyle \frac{\left ( \ln x \right )^{n}}{x}+C
  • x(\ln x)^{n-1}+C
  • x(\ln x)^{n}+C
  • none of these
What is the value of a + b ?
  • 2
  • 1
  • \frac{3}{2}
  • \frac{5}{2}
\displaystyle \int {\dfrac{dx}{\sin^2x \cos^2x}}
  • \tan x-\cot x+c
  • \tan x-x+1
  • \tan x-x
  • \tan x+x
If \displaystyle \int {\displaystyle  \frac { \sec^{ 2 }x-2010 }{ \sin^{ 2010 }x } dx=\displaystyle \frac { P(x) }{ (\sin x)^{ 2010 } } +c} , where c is arbitrary constant then value of P\left( \displaystyle \frac { \pi  }{ 3 }  \right)
  • 0
  • \displaystyle \frac { 1 }{ \sqrt { 3 } }
  • \sqrt { 3 }
  • \displaystyle \frac { 3\sqrt { 3 } }{ 2 }
0:0:3


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 12 Commerce Applied Mathematics Quiz Questions and Answers