The value of ${\int }_0^{\log 5}\frac{e^x.\sqrt{e^x-1}}{e^x+3} dx$ is

Important Questions on Definite Integrals and Their Properties

HARD

JEE Main

IMPORTANT

Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 8 - Definite Integrals and Their Properties>EXERCISE>Q 59

${\int }_0^{\infty }\frac{\log \left(x+{\displaystyle \frac{1}{x}}\right)}{1+x^2}dx=$

HARD

JEE Main

IMPORTANT

Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 8 - Definite Integrals and Their Properties>EXERCISE>Q 60

The value of ${\int }_0^{{\sin }^2 \theta }{\sin }^{-1} \sqrt{\varphi } d\varphi + {\int }_0^{{\cos }^2 \theta }{\cos }^{-1}\sqrt{\varphi } d\varphi$ is equal to

HARD

JEE Main

IMPORTANT

Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 8 - Definite Integrals and Their Properties>EXERCISE>Q 61

If $I={\int }_0^{\pi /2}\cos \left(\sin x\right) dx, J={\int }_0^{\pi /2}\sin \left(\cos x\right) dx and K={\int }_0^{\pi /2}\cos x dx,$ then

HARD

JEE Main

IMPORTANT

Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 8 - Definite Integrals and Their Properties>EXERCISE>Q 62

If $I_{10}={\int }_0^{\pi /2}{x}^{10}.\sin x dx,$ then the value of $I_{10}+90 I_8$ is

MEDIUM

JEE Main

IMPORTANT

Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 8 - Definite Integrals and Their Properties>EXERCISE>Q 1

${\int }_0^a\left(f\left(x\right)+f\left(-x\right)\right) dx=$

MEDIUM

JEE Main

IMPORTANT

Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 8 - Definite Integrals and Their Properties>EXERCISE>Q 2

If $f\left(x\right)=\left\{\begin{array}{l}{e}^{\cos x} \sin x, \left|x\right| \le 2\\ 2, \mathrm{otherwise}\end{array}\right.$ then ${\int }_{-2}^{3}f\left(x\right) dx=$

HARD

JEE Main

IMPORTANT

Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 8 - Definite Integrals and Their Properties>EXERCISE>Q 3

$\sqrt{3}{\int }_0^{\pi }\frac{dx}{1+2 {\sin }^2 x}=$

HARD

JEE Main

IMPORTANT

Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 8 - Definite Integrals and Their Properties>EXERCISE>Q 4

${\int }_0^{\infty }\frac{x.\log x}{{\left(1+x^2\right)}^2} dx=$