Fundamental theorem of calculus - class-XII
Description: fundamental theorem of calculus | |
Number of Questions: 26 | |
Created by: Prabha Kade | |
Tags: integrals mathematical tools elementary mathematics definite integral and it applications to areas applications of integration definite integration business maths definite integral definite integrals integral calculus maths physics |
The value of $\displaystyle \int _0^1\tan^{-1}\left (\frac {2x-1}{1+x-x^2}\right )dx$ is
$\int _{0}^{\pi /2}sin2xtan^{-1}\left ( sinx \right )dx=$
Evaluate: $\displaystyle \int _{0}^{\sqrt{3}}[x^{3} -1] dx$
$\displaystyle\int^{100} _0[\tan^{-1}x]dx$.
Solve $\displaystyle\int^{100} _0e^{x-[x]}dx=?$ where $[x]$ is greatest integer function.
$\int _0^\pi {{x^2}\,g\left( x \right)\,dx\, = } $
$\int _0^\pi {f\left( x \right)\,dx\, = } $
If $I _1 = \displaystyle \int^{2\pi /3} _{\pi / 2}\left|cos\dfrac{x}{2}cosx\right|dx,I _2=\left|\displaystyle \int _{\pi/2}^{2\pi/3} cos\dfrac{x}{2}cosxdx\right|$ then $I _1 - I _2$ equals
The value of the definite integral, $\displaystyle \int _0^{\pi/2} \dfrac{sin5x}{sinx}dx$ is
The value of the definite integral $\int _{ 0 }^{ \pi /2 }{ \sin { x } \sin { 2x } \sin { 3x } dx } $ is equal to:
The value of the integral $\displaystyle\int{\sin{x}{\cos}^{4}{x}dx}$ where $x\in\left[-1,\,1\right]$ is
If $\Delta (x)=\left| \begin{matrix} 1+x+2{ x }^{ 2 } & x+3 & 1 \ x+2{ x }^{ 2 } & x & 3 \ 3x+6{ x }^{ 2 } & 3x+11 & 9 \end{matrix} \right| $ then $\displaystyle \int^{1} _{0}\Delta (x)dx$ is
$\displaystyle \int _{1}^{4}\frac{\mathrm{x}\mathrm{d}\mathrm{x}}{\sqrt{2+4\mathrm{x}}}=$
The value of $\displaystyle \int _{0}^{2}(x-\log _{2}a)dx=2\log _{2}(\frac{2}{a})$ for which of the following conditions?
Consider the integral $I=\displaystyle\int^{\pi} _0 ln(\sin x)dx$.What is $\displaystyle\int^{\dfrac{\pi}{2}} _{0}$ ln $(\sin x)dx$ equal to?
Consider the integral $I=\displaystyle\int^{\pi} _0 ln(\sin x)dx$.What is $\displaystyle\int^{\frac{\pi} {2}} _0 ln(\cos x)dx$ equal to?
$ \int _{\sin x}^1 t^2 f(t) dt = 1 - \sin x \forall x \epsilon (0, \pi / 2 ) $ then $ f \left( \dfrac {1}{\sqrt3} \right) $ is :
Consider the integrals ${I _1} = \int _0^1 {{e^{ - x}}{{\cos }^2}xdx,} {I _2} = \int _0^1 {{e^{ - {x^2}}}{{\cos }^2}xdx,} {I _3} = \int _0^1 {{e^{ - x}}dx} $ and ${I _4} = \int _0^1 {{e^{ - (1/2){x^2}}}} dx$. The greatest of these integrals is
Let $ f\left( a,b \right) =\int _{ a }^{ b }{ \left( { x }^{ 2 }-4x+3 \right) dx,\left( b>a \right) }$ then
$\displaystyle \int _0^1 \dfrac{xe^x}{(x + 1)^2} dx =$
$\displaystyle\int _{ 0 }^{ 1 }{ \cfrac { \tan ^{ -1 }{ x } }{ x } } dx$ equals
Evaluate $\displaystyle\int^{\frac{3}{2}} _{-1}|x\sin(\pi x)|dx$.
$\int _{ 0 }^{ \infty }{ f\left( x+\cfrac { 1 }{ x } \right) .\cfrac { \ln { x } }{ x } } dx$
Evaluate $I = \displaystyle \int _{\pi /6}^{\pi /3}\sin x:dx$
What is $\displaystyle \int _{ 0 }^{ \pi }{ { e }^{ x } } \sin { x } dx$ equal to?