Application of Integrals

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JEE Main 2026 (Online) 8th April Evening ShiftQuestion 1

Let $f:(1,\infty)\to\mathbf{R}$ be a function defined as $f(x)=\frac{x-1}{x+1}$. Let $f^{i+1}(x)=f\left(f^{i}(x)\right)$, $i=1,2,\ldots,25$, where $f^{1}(x)=f(x)$. If $g(x)+f^{26}(x)=0$, $x\in(1,\infty)$, then the area of the region bounded by the curves $y=g(x)$, $2y=2x-3$, $y=0$ and $x=4$ is :

$\frac{1}{8}+\log_e2$$\frac{1}{4}+\log_e2$$\frac{5}{6}+3\log_e2$$\frac{5}{6}+\log_e2$

JEE Main 2021 (Online) 24th February Morning ShiftQuestion 2

The area (in sq. units) of the part of the circle $x^{2}+y^{2}=36$, which is outside the parabola $y^{2}=9x$, is :

Application of Integrals

$24\pi+3\sqrt{3}$$24\pi-3\sqrt{3}$$12\pi+3\sqrt{3}$$12\pi-3\sqrt{3}$

JEE Main 2026 (Online) 4th April Evening ShiftQuestion 3

The area of the region bounded by the curves $x+3y^{2}=0$ and $x+4y^{2}=1$ is equal to:

Application of Integrals

$\frac{1}{3}$$\frac{2}{3}$$\frac{4}{3}$$\frac{5}{3}$

JEE Main 2026 (Online) 6th April Evening ShiftQuestion 4

The area of the region $\{(x,y):x^{2}-8x\le y\le-x\}$ is :

Application of Integrals

$\frac{343}{6}$$\frac{637}{6}$$\frac{437}{6}$$\frac{523}{6}$

JEE Main 2024 (Online) 9th April Evening ShiftQuestion 5

The area (in square units) of the region enclosed by the ellipse $x^{2}+3y^{2}=18$ in the first quadrant below the line $y=x$ is

Application of Integrals

$\sqrt{3}\pi$$\sqrt{3}\pi-\frac{3}{4}$$\sqrt{3}\pi+\frac{3}{4}$$\sqrt{3}\pi+1$