JEE Main Maths · Application of Integrals

Area Between Curves

Area Between Curves (Application of Integrals) was asked 12 times in 12 JEE Main shifts, 2020–2026, out of the 42 shifts Lumi analysed. 3 of the 12 had a numerical answer.

Times asked: 12; in 12 shifts
Years: 2020–2026
Usual format: Single correct; Multi-step
Pattern: Asked most years; repeats across shifts

How it is asked

Area enclosed between two parabolas
Area bounded by conic and line

Difficulty

Easy 3Medium 4Hard 5

Where it sits

Chapter: Application of Integrals. Topic: Area Under Curves, 41 questions over 15 ideas.

All 12 questions

Newest first, each with its options and official answer.

2 Apr 2026, Shift 2 · Q24If the area of the region bounded by $16x^2 - 9y^2 = 144$ and $8x - 3y = 24$ is $A$ , then $3(A + 6\log_e(3))$ is equal toHardNumerical value
5 Apr 2026, Shift 2 · Q24Let $f:\mathbf{R}\to\mathbf{R}$ be a function such that $f(x)+3f\left(\frac{\pi}{2}-x\right)=\sin x$ , $x \in \mathbf{R}$ . Let the maximum…HardNumerical value
6 Apr 2026, Shift 1 · Q20Let $e$ be the base of natural logarithm and let $f:\{1,2,3,4\}\to\{1,e,e^2,e^3\}$ and…HardSingle correct
6 Apr 2026, Shift 2 · Q19The area of the region $\{(x,y): x^2-8x\le y\le -x\}$ is :EasySingle correct
8 Apr 2026, Shift 2 · Q18Let $f : (1, \infty) \to \mathbf{R}$ be a function defined as $f(x) = \frac{x-1}{x+1}$ . Let $f^{i+1}(x) = f\left(f^{i}(x)\right)$ ,…HardSingle correct
7 Apr 2025, Shift 1 · Q19If the area of the region bounded by the curves $y = 4 - \frac{x^2}{4}$ and $y = \frac{x-4}{2}$ is equal to $\alpha$ , then $6\alpha$ equalsEasySingle correct
31 Jan 2024, Shift 2 · Q11The area of the region enclosed by the parabolas $y=4x-x^2$ and $3y=(x-4)^2$ is equal toMediumSingle correct
29 Jun 2022, Shift 1 · Q6The area enclosed by $y^2 = 8x$ and $y = \sqrt{2}\,x$ that lies outside the triangle formed by $y = \sqrt{2}\,x$ , $x = 1$ ,…MediumSingle correct
3 Aug 2021, Shift 2 · Q85If the area (in sq. units) bounded by the parabolas $5x^2 - y = 0$ and $2x^2 - y + b = 0$ $(b > 0)$ is $12\sqrt{3}$ , then ' $b$ ' is equal…MediumNumerical value
16 Mar 2021, Shift 2 · Q80Let $C_1$ be the curve obtained by the solution of differential equation $2xy\frac{dy}{dx}=y^2-x^2$ , $x>0$ . Let the curve $C_2$ be the…HardSingle correct
9 Jan 2020, Shift 2 · Q63Given : $f(x)=\begin{cases}x, & 0\le x<\frac{1}{2}\\ \frac{1}{2}, & x=\frac{1}{2}\\ 1-x, & \frac{1}{2}<x\le1\end{cases}$ and…MediumSingle correct
6 Sep 2020, Shift 2 · Q62The area (in sq. units) of the region enclosed by the curves $y=x^2-1$ and $y=1-x^2$ is equal to :EasySingle correct