Definite Integration

Showing 36-40 of 392 questions.

Page 8 of 79

JEE Main 2021 (Online) 26th August Evening ShiftQuestion 36

If the value of the integral $\int_{0}^{5}\frac{x+[x]}{e^{x-[x]}}dx=\alpha e^{-1}+\beta$, where $\alpha,\beta\in\mathbf{R}$, $5\alpha+6\beta=0$, and $[x]$ denotes the greatest integer less than or equal to $x$; then the value of $(\alpha+\beta)^{2}$ is equal to :

$25$$36$$100$$16$

JEE Main 2023 (Online) 15th April Morning ShiftQuestion 37

If $\int_{0}^{1}\frac{1}{\left(5+2x-2x^{2}\right)\left(1+e^{(2-4x)}\right)}dx=\frac{1}{\alpha}\log_e\left(\frac{\alpha+1}{\beta}\right)$, $\alpha,\beta>0$, then $\alpha^{4}-\beta^{4}$ is equal to

Definite Integration

$-21$$0$$19$$21$

JEE Main 2024 (Online) 31st January Evening ShiftQuestion 38

Let $f,g:(0,\infty)\to\mathbb{R}$ be two functions defined by $f(x)=\int_{-x}^{x}\left(|t|-t^{2}\right)e^{-t^{2}}dt$ and $g(x)=\int_{0}^{x^{2}}t^{1/2}e^{-t}dt$. Then, the value of $9\left(f\left(\sqrt{\log_e9}\right)+g\left(\sqrt{\log_e9}\right)\right)$ is equal to

Definite Integration

$8$$6$$9$$10$

JEE Main 2023 (Online) 13th April Evening ShiftQuestion 39

The value of $\frac{e^{-\frac{\pi}{4}}+\int_{0}^{\pi/4}e^{-x}\tan^{50}x\,dx}{\int_{0}^{\pi/4}e^{-x}\left(\tan^{49}x+\tan^{51}x\right)dx}$ is

Definite Integration

$25$$49$$50$$51$

JEE Main 2021 (Online) 27th August Morning ShiftQuestion 40

$\int_{6}^{16}\frac{\log_ex^{2}}{\log_ex^{2}+\log_e\left(x^{2}-44x+484\right)}dx$ is equal to :

Definite Integration

$10$$8$$6$$5$