Definite Integration

Showing 51-55 of 392 questions.

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JEE Main 2024 (Online) 30th January Evening ShiftQuestion 51

Let $f:\mathbb{R}\to\mathbb{R}$ be a function defined by $f(x)=\frac{x}{\left(1+x^{4}\right)^{1/4}}$, and $g(x)=f(f(f(f(x))))$. Then, $18\int_{0}^{\sqrt{2\sqrt{5}}}x^{2}g(x)\,dx$ is equal to

$33$$42$$36$$39$

JEE Main 2024 (Online) 1st February Evening ShiftQuestion 52

If $\int_{0}^{\pi/3}\cos^{4}x\,dx=a\pi+b\sqrt{3}$, where $a$ and $b$ are rational numbers, then $9a+8b$ is equal to :

Definite Integration

$3$$2$$\frac{3}{2}$$1$

JEE Main 2025 (Online) 4th April Morning ShiftQuestion 53

The value of $\int_{-1}^{1}\frac{\left(1+\sqrt{|x|-x}\right)e^{x}+\left(\sqrt{|x|-x}\right)e^{-x}}{e^{x}+e^{-x}}dx$ is equal to

Definite Integration

$2+\frac{2\sqrt{2}}{3}$$3-\frac{2\sqrt{2}}{3}$$1-\frac{2\sqrt{2}}{3}$$1+\frac{2\sqrt{2}}{3}$

JEE Main 2024 (Online) 6th April Morning ShiftQuestion 54

$\int_{0}^{\pi/4}\frac{\cos^{2}x\sin^{2}x}{\left(\cos^{3}x+\sin^{3}x\right)^{2}}dx$ is equal to

Definite Integration

$\frac{1}{3}$$\frac{1}{6}$$\frac{1}{9}$$\frac{1}{12}$

JEE Main 2024 (Online) 30th January Evening ShiftQuestion 55

Let $a$ and $b$ be real constants such that the function $f$ defined by $f(x)=\begin{cases}x^{2}+3x+a, & x\le1\\ bx+2, & x>1\end{cases}$ be differentiable on $\mathbb{R}$. Then, the value of $\int_{-2}^{2}f(x)\,dx$ equals

Definite Integration

$\frac{15}{6}$$\frac{19}{6}$$17$$21$