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CBSE Questions for Class 12 Commerce Applied Mathematics Indefinite Integrals Quiz 2 - MCQExams.com

sin1(cosx)dx is equal to
  • πx2+c
  • πx22+c
  • πxx22+c
  • πx+x22+c
What is dxx(1+lnx)n equal to (n1) ?
  • 1(n1)(1+lnx)n1+c
  • 1n(1+lnx)1n+c
  • n+1(1+lnx)n+1+c
  • 1(n1)(1+lnx)n1+c
Evaluate xsecx.tanxdx=
  • xsecx+log|tan(π/2+x/2)|+c
  • xsecxlog|tan(π/4+x/2)|+c
  • xsecxlog|tan(π/4+x)|+c
  • xsecx+log|tanx/2|+c
\displaystyle \int\{\frac{(\log x-1)}{1+(\log x)^{2}}\}^{2}dx is equal to
  • \displaystyle \frac{x}{(\log x)^{2}+1}+c
  • \displaystyle \frac{xe^{x}}{1+x^{2}}+c
  • ^{\dfrac{x}{x^{2}+1}+c}
  • \displaystyle \frac{\log x}{(\log x)^{2}+1}+c
\displaystyle \int \sec^{2}x.\text{cosec}^{2}xdx=
  • \tan x-\cot x +c
  • \tan x +\cot x +c
  • -\tan x + \cot x +c
  • \sec x \tan x +c
\displaystyle \int\sqrt{\frac{x}{x-1}}dx, x\in(0,\pi/2) equals
  • \sqrt{x(x-1)}+\log(\sqrt{x}+\sqrt{x-1})+c
  • \sqrt{x(x-1)}-\log(\sqrt{x}+\sqrt{x-1})+c
  • \sqrt{x(x-1)}+\log(\sqrt{x}-\sqrt{x-1})+c
  • \sqrt{x(x+1)}-\log(\sqrt{x}-\sqrt{x+1})+c
\displaystyle \int xe^{2x}(1+x)dx equal to

  • \displaystyle \frac{xe^{x}}{2}+c
  • \displaystyle \frac{(e^{x})^{2}}{2}r
  • \displaystyle \frac{(1+x)^{2}}{2}+c
  • \displaystyle \frac{(xe^x)^2}{2}
The value of \displaystyle \int x^{2}2^{3x}dx=
  • \displaystyle \frac{x^{2}2^{3x}}{4\log 2}-\frac{x.2^{3x+1}}{9.(\log 2)^3}+\frac{2^{3x+1}}{27(\log 2)}+c
  • \displaystyle \frac{x^{2}2^{3x}}{3\log 2}-\frac{x.2^{3x+1}}{9.(\log 2)}+\frac{2^{3x+1}}{27(\log 2)}+c
  • \displaystyle \frac{x^{2}2^{3x}}{3\log 2}-\frac{2^{3x+1}.x}{3^{2}(\log 2)^{2}}+\frac{2^{3x+1}}{3^{3}(\log 2)^{3}}+c
  • \displaystyle \frac{x^{2}2^{3x}}{\log 2}-\frac{2^{3x+1}.x}{3^{2}(\log 2)^{2}}+\frac{2^{3x+1}}{(\log 2)^{3}}+c
\displaystyle \int\log{x}d{x}=
  • x(\log x-x)+c
  • x(\log x)+c
  • x(\log x-1)+c
  • x(\log x+x)+c
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[\frac{cosx}{x}-\sin{x}\log x]dx=
  • (\log x) sinx+c
  • (\log x) (cos x) +c
  • 2(\log x) (cos x) +c
  • -(\log x) sin x+c
Evaluate \displaystyle \int x^{2}e^{x}dx=
  • e^{x}(x^{2}-2x+2)+c
  • e^{x}(x^{2}+2x+2)+c
  • x^{2}+ex+c
  • e^{x}(x^{2}+x+2)+c
\displaystyle \int e^{\log x}\cos xdx=
  • xsinx-cosx+c
  • \dfrac{x}{2}sinx+cos^{2}x+c
  • xsinx+cosx+c
  • xsinx+sinx+c
\displaystyle \int\frac{x\cos x\log x-\sin x}{x(\log x)^{2}}dx is equal to
  • \displaystyle \frac{\sin x}{\log x}+c
  • \log{x}+\sin{x+c}
  • \log{x}\sin{x+c}
  • \displaystyle \frac{\cos x}{\log x}+c
The value of \int x(cosecx\ cotx)dx= is
  • xcosec x-log |tanx/2|+c
  • 2-xcosec x+\log| tan \displaystyle \frac{x}{2}|+c
  • xcosec x-2 \log|tanx/2|+c
  • xcot x-log |tan{\displaystyle \frac{x}{2}}|+c
Solve  \displaystyle \int \tan^{-1}xdx
  • x\tan x -\log|1+x^{2}|+c
  • x \tan^{-1} x -\displaystyle \frac{1}{2}\log|1+x^{2}|+c
  • x  \tan^{-1} x+\log\sqrt{1+x^{2}}+c
  • x\tan x+\log|1+x^{2}|+c
Evaluate \displaystyle \int\frac{\log(x/e)}{(\log x)^{2}}dx
  • \displaystyle \frac{\log x}{x}+c
  • \displaystyle \frac{x}{\log x}+c
  • ^{\dfrac{x}{log(x)^{2}}+c}
  • \displaystyle \frac{(\log x)^{2}}{x}+c
\displaystyle \int x^{2} {\it cosh} 4xdx=
  • \displaystyle \frac{x^{2}}{4} {\it sinh}4x-\displaystyle \frac{x}{8}{\it cosh} 4x+\displaystyle \frac{\sinh 4x}{32}+c
  • \displaystyle \frac{x^{2}}{4}sinh4x+\frac{x}{8} cosh 4{x-}\displaystyle \frac{\sinh 4x}{32}+c
  • \displaystyle \frac{x^{2}}{4}sinh4x-\frac{x}{8} cosh 4x-\displaystyle \frac{\sinh 4x}{32}+c
  • \displaystyle \frac{x^{2}}{4}sinh4x+\frac{x}{8} cosh 4x-\displaystyle \frac{\sin h4x}{64}+
\displaystyle \int cot^{-1}(\frac{x-1}{x+1})dx=
  • \displaystyle \frac{\pi}{4}x+x\cot^{-1}x-\frac{1}{2}\log(1+x^{2})+c
  • x\displaystyle \cot^{-1}x+\frac{1}{2}\log(1+x^{2})+c
  • \displaystyle \frac{\pi}{4}x-\frac{1}{2}\log(1+x^{2})+c
  • ^{\displaystyle \frac{\pi}{4}x+x\cot^{-1}x}+\displaystyle \frac{1}{2}\log(1+x^{2})+c
\displaystyle \int e^{x}cosec x(1-\cot x)dx=
  • e^{x}\cot x+c
  • e^{x}cosec x\cot x+c
  • e^{x}cosec x+c
  • -e^{x}\cot x+c
\displaystyle \int x^{2}a^{x}dx=
  • a^{x}[\displaystyle \frac{x^{2}}{\log a}-\frac{2x}{(\log a)^{2}}+\frac{2}{(\log a)^{3}}]+c
  • a^{x}[\displaystyle \frac{x^{2}}{\log a}+\frac{2x}{(\log a)^{2}}-\frac{2}{(\log a)^{3}}]+c
  • a^{x}[\displaystyle \frac{x^{2}}{\log a}+\frac{2x}{(\log a)^{2}}+\frac{2}{(\log a)^{3}}]+c
  • a^{x}(\displaystyle \frac{x}{\log a}-\frac{1}{(\log a)^{2}})+c
lf polynomials P and Q satisfy \displaystyle{\int((3x-1)\cos x+(1-2x)\sin x)dv}=P\cos x+Q\sin x+R (ignoring the constant of integration) then
  • P=3x-2
  • Q=2+x
  • P=3(x-1)
  • Q=3(x-1)
Evaluate \displaystyle \int\frac{\arcsin\sqrt{x}}{\sqrt{1-x}}dx =
  • 2[\sqrt{x}-\sqrt{1-x} arc \sin\sqrt{x}]+c
  • 2[\sqrt{x}+\sqrt{1-x} arc \sin\sqrt{x}]+c
  • 2[\sqrt{x}+\sqrt{1-x} arc \cos\sqrt{x}]+c
  • 2[\sqrt{x}-\sqrt{1-x} arc \cos\sqrt{x}]+c
\displaystyle \int e^{x}(x^{2}-5x+8) dx =e^{x}f(x)+c then f(x)
  • x^{2}-5x+12
  • x^{2}+7x+15
  • x^{2}-7x-15
  • x^{2}-7x+15

Evaluate \displaystyle \int x\frac{(\sec 2x-1)}{(\sec 2x+1)}dx
  • x \tan x-\log |\displaystyle \sec x|+\frac{x^{2}}{2}+c
  • x \tan x-\log |\displaystyle \sec x|-\frac{x^{2}}{2}+c
  • x \tan x-\log |\sec\frac{x}{2}|+c
  • x \tan x-\log |\displaystyle \sec\frac{x}{2}|+\frac{x^{2}}{2}+c
\displaystyle \int e^{x}2^{3\log_{2}x}dx=e^{x}f(x)+c, then f(x)=
  • { x }^{ 3 }-3{ x }^{ 2 }+6x-6
  • x^{3}-3x^{2}-6x-3
  • x^{3}-3x^{2}+6x+6
  • x^{3}+3x^{2}+6x+6
\displaystyle \int\frac{x+\sin x}{1+\cos x}dx=
  • xtan \displaystyle \frac{x}{2}+c
  • xcot \displaystyle \frac{x}{2}+c
  • xsin \displaystyle \frac{x}{2}+c
  • xcos \displaystyle \frac{x}{2}+c
\displaystyle \int\cos^{-1}(\frac{1}{x})dx equal to
  • x\sec^{-1}x+\cosh^{-1}x+c
  • x\sec^{-1}x-\cosh^{-1}x+c
  • x\sec^{-1}x-\sin^{-1}x+c
  • x\sec^{-1}x+\sin^{-1}x+c
Evaluate: \displaystyle \int\log_{10}xdx
  • (x-1)\log_{e}x+c
  • \displaystyle \log_{e}10.x\log_{e}(\frac{x}{e})+c
  • \displaystyle \log_{10}e.x\log_{e}(\frac{x}{e})+c
  • \cfrac{1}{x}+c
Evaluate \displaystyle \int\frac{xe^{x}}{(x+1)^{2}}dx
  • \displaystyle e^{x}[\dfrac{1}{x+1}]+c
  • \displaystyle e^{x}[\dfrac{-1}{x+1}]+c
  • e^{x}x+c
  • \displaystyle e^{x}[\dfrac{-1}{(x+1)^{2}}]+c
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Practice Class 12 Commerce Applied Mathematics Quiz Questions and Answers