Definite Integration

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JEE Main 2026 (Online) 6th April Evening ShiftQuestion 11

The value of the integral $\int_{-1}^{1}\left(\frac{x^{3}+|x|+1}{x^{2}+2|x|+1}\right)dx$ is equal to :

Definite Integration

$3\log_e2$$2\log_e2$$5\log_e3$$3\log_e3$

JEE Main 2021 (Online) 26th February Evening ShiftQuestion 12

For $x>0$, if $f(x)=\int_{1}^{x}\frac{\log_et}{(1+t)}dt$, then $f(e)+f\left(\frac{1}{e}\right)$ is equal to :

Definite Integration

$0$$1$$\frac{1}{2}$$-1$

JEE Main 2021 (Online) 24th February Evening ShiftQuestion 13

Let $f(x)$ be a differentiable function defined on $[0,2]$ such that $f'(x)=f'(2-x)$ for all $x\in(0,2)$, $f(0)=1$ and $f(2)=e^{2}$. Then the value of $\int_{0}^{2}f(x)\,dx$ is :

Definite Integration

$1-e^{2}$$1+e^{2}$$2\left(1+e^{2}\right)$$2\left(1-e^{2}\right)$

JEE Main 2021 (Online) 25th July Morning ShiftQuestion 14

The value of the definite integral $\int_{\pi/24}^{5\pi/24}\frac{dx}{1+\sqrt[3]{\tan2x}}$ is :

Definite Integration

$\frac{\pi}{18}$$\frac{\pi}{3}$$\frac{\pi}{12}$$\frac{\pi}{6}$

JEE Main 2021 (Online) 26th August Morning ShiftQuestion 15

The value of $\int_{-1/\sqrt{2}}^{1/\sqrt{2}}\left(\left(\frac{x+1}{x-1}\right)^{2}+\left(\frac{x-1}{x+1}\right)^{2}-2\right)^{1/2}dx$ is :

Definite Integration

$4\log_e\left(3+2\sqrt{2}\right)$$\log_e4$$\log_e16$$2\log_e16$