Application of Integrals

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JEE Main 2022 (Online) 26th July Evening ShiftQuestion 6

The area bounded by the curves $y=|x^2-1|$ and $y=1$ is

Application of Integrals

$\frac23(\sqrt2+1)$$\frac43(\sqrt2-1)$$2(\sqrt2-1)$$\frac83(\sqrt2-1)$

JEE Main 2023 (Online) 11th April Morning ShiftQuestion 7

Area of the region $\left\{(x,y):x^{2}+(y-2)^{2}\le4,\ x^{2}\ge2y\right\}$ is

Application of Integrals

$\pi-\frac{8}{3}$$2\pi-\frac{16}{3}$$\pi+\frac{8}{3}$$2\pi+\frac{16}{3}$

JEE Main 2023 (Online) 13th April Morning ShiftQuestion 8

The area of the region enclosed by the curve $f(x)=\max\{\sin x,\cos x\}$, $-\pi\le x\le\pi$ and the $x$-axis is

Application of Integrals

$2\sqrt{2}\left(\sqrt{2}+1\right)$$4$$2\left(\sqrt{2}+1\right)$$4\left(\sqrt{2}\right)$

JEE Main 2020 (Online) 8th January Evening ShiftQuestion 9

The area (in sq. units) of the region $\{(x,y)\in\mathbf{R}^2:x^2\le y\le3-2x\}$, is :

Application of Integrals

$\frac{32}3$$\frac{29}3$$\frac{31}3$$\frac{34}3$

JEE Main 2020 (Online) 2nd September Evening ShiftQuestion 10

Consider a region $R=\{(x,y)\in\mathbf{R}^2:x^2\le y\le2x\}$. If a line $y=\alpha$ divides the area of region $R$ into two equal parts, then which of the following is true ?

Application of Integrals

$3\alpha^2-8\alpha+8=0$$\alpha^3-6\alpha^2+16=0$$3\alpha^2-8\alpha^{3/2}+8=0$$\alpha^3-6\alpha^{3/2}-16=0$