Definite Integration

Chapter overview and full question list

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JEE Main 2021 (Online) 27th August Evening ShiftQuestion 31

The value of the integral $\int_{0}^{1}\frac{\sqrt{x}\,dx}{(1+x)(1+3x)(3+x)}$ is :

Definite Integration

$\frac{\pi}{8}\left(1-\frac{\sqrt{3}}{2}\right)$$\frac{\pi}{8}\left(1-\frac{\sqrt{3}}{6}\right)$$\frac{\pi}{4}\left(1-\frac{\sqrt{3}}{6}\right)$$\frac{\pi}{4}\left(1-\frac{\sqrt{3}}{2}\right)$

JEE Main 2024 (Online) 9th April Evening ShiftQuestion 32

The integral $\int_{1/4}^{3/4}\cos\left(2\cot^{-1}\sqrt{\frac{1-x}{1+x}}\right)dx$ is equal to

Definite Integration

$\frac{1}{4}$$-\frac{1}{4}$$\frac{1}{2}$$-\frac{1}{2}$

JEE Main 2024 (Online) 1st February Morning ShiftQuestion 33

The value of the intergral $\int_{0}^{\pi/4}\frac{x\,dx}{\sin^{4}(2x)+\cos^{4}(2x)}$ equals :

Definite Integration

$\frac{\sqrt{2}\pi^{2}}{16}$$\frac{\sqrt{2}\pi^{2}}{32}$$\frac{\sqrt{2}\pi^{2}}{8}$$\frac{\sqrt{2}\pi^{2}}{64}$

JEE Main 2025 (Online) 4th April Evening ShiftQuestion 34

Let $f(x)+2f\left(\frac{1}{x}\right)=x^{2}+5$ and $2g(x)-3g\left(\frac{1}{2}\right)=x$, $x>0$. If $\alpha=\int_{1}^{2}f(x)\,dx$, and $\beta=\int_{1}^{2}g(x)\,dx$, then the value of $9\alpha+\beta$ is :

Definite Integration

$0$$1$$10$$11$

JEE Main 2023 (Online) 11th April Evening ShiftQuestion 35

If $f:\mathbb{R}\to\mathbb{R}$ be a continuous function satisfying $\int_{0}^{\pi/2}f(\sin2x)\sin x\,dx+\alpha\int_{0}^{\pi/4}f(\cos2x)\cos x\,dx=0$, then the value of $\alpha$ is

Definite Integration

$-\sqrt{2}$$\sqrt{2}$$-\sqrt{3}$$\sqrt{3}$