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CBSE Questions for Class 12 Commerce Maths Integrals Quiz 1 - MCQExams.com

Let F(x)=f(x)+f(1x), where f(x)=xllogtl+tdt. Then F(e) equals
  • 12
  • 0
  • 1
  • 2
The following integral π/2π/4(2cosecx)17dx is equal to
  • log(1+2)02(eu+eu)16du
  • log(1+2)02(eu+eu)17du
  • log(1+2)02(eueu)17du
  • log(1+2)02(eueu)16du
The value of g(12) is?
  • π
  • 2π
  • π2
  • π4
\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)
\int \dfrac {dx}{\sqrt {x^{10} - x^{2}}}; x > 1= ______ + C.
  • \dfrac {1}{4}\log |\sqrt {x^{10} - x^{2}} + x^{2}|
  • \dfrac {1}{2}\log |x^{10} - x^{2}|
  • -\dfrac {1}{4}\sec^{-1} (x^{4})
  • \dfrac {1}{4}\sec^{-1} (x^{4})
Evaluate the integral
\displaystyle \int_{0}^{1}\frac{1}{1+x^{2}}dx
  • \pi/4
  • \pi
  • \pi/3
  • 0
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
 Find \displaystyle\int_0^\dfrac{\pi}{2}{cos^3}{x}\ dx
  • \dfrac{2}{3}
  • 2
  • 1
  • -2
\displaystyle  \int _{ 0 }^{ 1 }{ \tan ^{ -1 }{ \left( \dfrac { x }{ \sqrt { 1-{ x }^{ 2 } }  }  \right)  } dx }
  • \dfrac{\pi}{2}
  • \dfrac{\pi}{2}-1
  • 0
  • None of these
\int _{ 0 }^{ 1 }{ \dfrac { { e }^{ x }.x }{ { \left( x+1 \right)  }^{ 2 } } dx= }
  • \dfrac{e}{2}
  • 1+\dfrac{e}{2}
  • \dfrac{e}{2}-1
  • 1-\dfrac{e}{2}
Find \int\limits_0^{\sqrt 2 } {\sqrt {2 - {x^2}} dx}
  • \frac{\pi }{2}
  • 8
  • 0
  • 2
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
Evaluate \displaystyle\int^{3}_{2}3^{x}dx
  • \dfrac{1}{\ln 3}
  • \dfrac{8}{\ln 3}
  • \dfrac{18}{\ln 3}
  • None of these
\int_0^{ \pi /2 } \sin^5 x \cos ^6 x dx =
  • \dfrac {8}{693}
  • \dfrac {32}{693}
  • \dfrac {8}{99}
  • \dfrac {16}{63}
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 
\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
\displaystyle \int_{\pi /4}^{3\pi/4 }\dfrac{dx}{1+\cos x} is equal to 
  • -2
  • 2
  • 4
  • -1
\int \sin ^{-1}(\cos x) d x  is equal to
  • \frac{\pi x}{2}+c
  • \frac{\pi x^{2}}{2}+c
  • \frac{\pi x-x^{2}}{2}+c
  • \frac{\pi x+x^{2}}{2}+c
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
What is \displaystyle \int \dfrac{dx}{x(1 + ln x)^n} equal to (n \neq 1) ?
  • \dfrac{1}{(n - 1)(1 + ln x)^{n - 1}} + c
  • \dfrac{1 - n}{(1 + ln x)^{1- n}} + c
  • \dfrac{n + 1}{(1 + ln x)^{n+1}} + c
  • -\dfrac{1}{(n - 1)(1 + ln x)^{n-1}} + c
Evaluate \displaystyle\int^1_0\dfrac{1}{(1+x^2)}dx
  • \dfrac{\pi}{2}
  • \dfrac{\pi}{3}
  • \dfrac{\pi}{4}
  • None of these
Evaluate the integral
\displaystyle \int_{1}^{e^{3}}\frac{dx}{x\sqrt{1+\ln x}}
  • 2
  • 2\sqrt{2}
  • \sqrt{2}
  • -2
The integral \displaystyle \int_{0}^{\pi_/{3}}\frac{\cos x}{3+4\sin x}d_{X=}
  • \displaystyle \log\left(\frac{3+2\sqrt{3}}{3}\right)
  • \dfrac{1}{4} \log\left(\displaystyle \frac{3+2\sqrt{3}}{3}\right)
  • 2\displaystyle \log\left(\frac{3+2\sqrt{3}}{3}\right)
  • \dfrac{1}{2}\log\left(\displaystyle \frac{3+2\sqrt{3}}{2}\right)
Evaluate the integral
\displaystyle \int_{0}^{\pi_/{2}}\frac{cosx}{1+sin^{2}x}dx
  • \pi
  • \pi/3
  • \pi/2
  • \pi/4

\displaystyle \int_{-1}^{3}\left( \tan^{ -1 }\frac { x }{ x^{ 2 }+1 } +\tan ^{ -1 } \frac { x^{ 2 }+1 }{ x }  \right) dx=
  • \pi
  • 2\pi
  • 4\pi
  • 3\pi
If \displaystyle \int_{1/\sqrt{3}}^{k}\dfrac{1}{1+x^{2}}dx= \dfrac{\pi}{6} 
then the upper limit k=?
  • \sqrt{3}
  • \displaystyle \frac{1}{\sqrt{3}}
  • 1
  • 2+\sqrt{3}
The integral \displaystyle \int_{0}^{\pi/4}\frac{\sin^{9}x}{\cos^{11}x}dx=
  • 10
  • 5
  • \dfrac{1}{10}
  • \dfrac{1}{5}
\displaystyle \int_{0}^{1}\frac{4x^{3}}{\sqrt{1-x^{8}}}dx =?
  • \pi
  • -\pi
  • \pi /2
  • - \pi /2
Evaluate: \displaystyle \int_{0}^{1}\frac{\tan^{-1}x}{1+x^{2}}dx
  • \displaystyle \frac{\pi^{2}}{4}
  • \displaystyle \frac{\pi^{2}}{18}
  • \displaystyle \frac{\pi^{2}}{32}
  • \displaystyle \frac{\pi^{2}}{8}-1
Evaluate: \displaystyle \int_{1}^{2}\frac{1}{x\sqrt{x^{2}-1}}d{x}
  • \pi
  • \dfrac {\pi}{2}
  • \dfrac {\pi}{4}
  • \dfrac {\pi}{3}

\displaystyle \int_{0}^{\pi_/{2}}\frac{\cos x}{1+\sin x}d_{X=}
  • \log 2
  • \log \mathrm{e}
  • \dfrac{1}{2} log3
  • 0
The value of \int_{0}^{\infty} x.e^{-x^{2}}dx_{=}
  • 1
  • - 1/2
  • 1/2
  • 0
\displaystyle \int_{0}^{1}\frac{x^{2}}{1+x^{2}}dx equals
  • 1-\displaystyle \frac{\pi}{4}
  • 1-\displaystyle \frac{\pi}{3}
  • \displaystyle \frac{\pi}{3}
  • \displaystyle \frac{\pi}{4}

\displaystyle \int_{0}^{1}\frac{dx}{e^{x}+e^{-x}}=
  • tan^{-1}e
  • \displaystyle \frac{\pi}{4}
  • ta\displaystyle \mathrm{n}^{-1}\mathrm{e}-\frac{\pi}{4}
  • ta\displaystyle \mathrm{n}^{-1}\mathrm{e}+\frac{\pi}{4}

\displaystyle \int_{1}^{2}(\frac{1+x\log x}{x})e^{x}dx_{=}
  • \mathrm{e}^{2} log2
  • elog2
  • \displaystyle \frac{1}{2} log2
  • \displaystyle \frac{\mathrm{e}^{2}}{2} log2
Evaluate the integral
\displaystyle \int_{\frac{\sqrt{2}}{3}}^{ \frac{\sqrt{3}}{3}}\displaystyle \frac{dx}{\sqrt{4-9x^{2}}}
  • \displaystyle \frac{\pi}{36}
  • \displaystyle \frac{\pi}{3}
  • \displaystyle \frac{\pi}{4}
  • \displaystyle \frac{7\pi}{30}
\displaystyle \int_{0}^{\pi /2} \displaystyle \frac{1}{\sin x+\cos x} \ dx
  • \sqrt{2}l\mathrm{o}\mathrm{g}(\sqrt{2}+1)
  • \sqrt{2}l\mathrm{o}\mathrm{g}(\sqrt{2}-1)
  • \dfrac{1}{\sqrt{2}}l\mathrm{o}\mathrm{g}(\sqrt{2}+1)
  • \dfrac{-1}{\sqrt{2}}l\mathrm{o}\mathrm{g}(\sqrt{2}+1)
Evaluate the integral
\displaystyle \int_{0}^{\pi_/{2}}\cos^{5}x.\sin 2xdx
  • 2/7
  • 1/7
  • -1/7
  • 3/7

\displaystyle \int_{0}^{\displaystyle \tfrac{\pi}{4}}\sqrt{\frac{1-\sin 2x}{1+\sin 2x}}dx=
  • \log 2
  • -\log\sqrt{2}
  • 2\log 2
  • 3\log\sqrt{2}
\int_{\pi /4}^{\pi /2} Cotx.dx_{=}
  • 2 log 2
  • \displaystyle \frac{\pi}{2} log2
  • \log\sqrt{2}
  • \log 2
Evaluate the integral
\displaystyle \int_{0}^{1}\frac{dx}{\sqrt{1-x^{2}}}
  • 0
  • -1
  • \pi/2
  • -\pi/2
Evaluate the integral
\displaystyle \int_{0}^{1}\frac{(\sin^{-1} {x})^{2}}{\sqrt{1-x^{2}}}dx
  • \displaystyle \frac{\pi^{3}}{24}
  • \pi^{2}
  • -\pi^{2}
  • 0
Evaluate the integral
\displaystyle \int_{0}^{a}\sqrt{a^{2}-x^{2}}dx
  • \displaystyle \frac{a^{2}}{4}
  • \pi {a}^{2}
  • \displaystyle \frac{\pi a^{2}}{2}
  • \displaystyle \frac{\pi a^{2}}{4}
Evaluate the integral
\displaystyle \int_{1/2}^{1}\frac{1}{\sqrt{1-x^{2}}}dx
  • \pi
  • \pi/2
  • \pi/3
  • \pi/4

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

\displaystyle \int_{0}^{a}\frac{1}{a^{2}+x^{2}}dx_{=}
  • \pi/2
  • \pi/3
  • \pi/4
  • \pi/4a
Evaluate the integral
\displaystyle \int_{\frac{a}{2}}^{a}\frac{1}{\sqrt{a^{2}-x^{2}}}dx
  • \dfrac{\pi}{2}
  • \pi a
  • \pi-1
  • \dfrac{\pi}{3}
Evaluate the integral
\displaystyle \int_{0}^{1}\frac{x}{1+x^{2}}dx
  • \log 2
  • \displaystyle \frac{1}{2} \log2 
  • 2
  • \log 4

The integral \displaystyle \int_{0}^{1}\frac{x^{3}}{1+x^{8}}dx=
  • \dfrac{\pi}{16}
  • \dfrac{\pi}{4}
  • \dfrac{\pi}{2}
  • \dfrac{\pi}{8}

\displaystyle \int_{0}^{1}\frac{1}{1+x}dx_{=}
  • \log 2
  • \displaystyle \frac{1}{2} \log2
  • 2
  • \log 3
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