JEE Main Maths · Application of Integrals

Area Under Curves in JEE Main

Name: Area Under Curves: JEE Main previous year questions
Creator: Lumi

Area Under Curves (Maths, Application of Integrals) came 41 times in 38 of the 42 JEE Main shifts Lumi analysed, across 15 distinct ideas. 25 of them came in 2024–26; it was last asked in 2026.

Questions: 41; in 38 shifts
Ideas asked: 15; 4 asked more than once
Numerical answer: 12; 29% of its questions
Pattern: Asked most years; last asked 2026

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 5Medium 20Hard 16

Format

Single correct29 Q
Numerical value12 Q

Ideas inside the topic

15 ideas

Area Between Curves12 Q
Area of Inequalities10 Q
Area Involving Max/Min Functions6 Q
Ratio of Divided Areas2 Q
Bisection of Bounded Areas1 Q
Curves from Area Properties1 Q
Ellipse Segment Area via Eccentric Angle1 Q
Area of Ellipse and its Segments1 Q
Area of Ellipse and Sectors1 Q
Area of Locus-Defined Regions1 Q
Area with Modulus1 Q
Regions with Multiple Bounding Curves1 Q

Where it sits

Part of Application of Integrals, which had 39 questions in all. Area Under Curves accounts for 105% of them. In Lumi's JEE taxonomy it belongs to Calculus.

Some questions sit in other chapters too: Conic Sections, Differential Equations.

Every question

All 41 Area Under Curves 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
4 Apr 2026, Shift 1 · Q18The area of the region $\{(x,y): y\le\pi-|x|,\ y\le|x\sin x|,\ y\ge0\}$ is:HardSingle correct
4 Apr 2026, Shift 2 · Q18The area of the region bounded by the curves $x+3y^2=0$ and $x+4y^2=1$ is equal to:EasySingle correct
5 Apr 2026, Shift 1 · Q16The area of the region $R = \{(x, y) : xy \leq 27,\ 1 \leq y \leq x^2\}$ is equal to:MediumSingle correct
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 · Q19The area of the region $\{(x,y): 0\le y\le 6-x,\ y^2\ge 4x-3,\ x\ge 0\}$ is:MediumSingle correct
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
2 Apr 2025, Shift 1 · Q21If the area of the region $\left\{(x, y): \left|4-x^2\right|\le y\le x^2,\ y\le4,\ x\ge0\right\}$ is…HardNumerical value
3 Apr 2025, Shift 1 · Q25The area of the region bounded by the curve $y = \max\{|x|, x|x-2|\}$ , the $x$ -axis and the lines $x = -2$ and $x = 4$ is equal to ______MediumNumerical value
3 Apr 2025, Shift 2 · Q19The area of the region $\left\{(x, y) : |x - y| \leq y \leq 4\sqrt{x}\right\}$ isMediumSingle correct
4 Apr 2025, Shift 2 · Q19A line passing through the point $A(-2,0)$ , touches the parabola $P:y^2=x-2$ at the point B in the first quadrant. The area, of the region…MediumSingle 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
7 Apr 2025, Shift 2 · Q20If the area of the region $\{(x,y): 1+x^2\le y\le \min\{x+7,\ 11-3x\}\}$ is $A$ , then $3A$ is equal toMediumSingle correct
8 Apr 2025, Shift 2 · Q25Let the area of the bounded region $\{(x, y) : 0 \le 9x \le y^2, y \ge 3x - 6\}$ be $A$ . Then $6A$ is equal to __________MediumNumerical value
6 Apr 2024, Shift 2 · Q11If the area of the region $\left\{(x,y):\frac{a}{x^2}\le y\le\frac{1}{x},\ 1\le x\le 2,\ 0<a<1\right\}$ is $(\log_e 2)-\frac{1}{7}$ then…MediumSingle correct
8 Apr 2024, Shift 1 · Q12Let $f(x)$ be a positive function such that the area bounded by $y=f(x)$ , $y=0$ from $x=0$ to $x=a>0$ is $e^{-a}+4a^2+a-1$ . Then the…HardSingle correct
8 Apr 2024, Shift 1 · Q27Let the area of the region enclosed by the curve $y=\min\{\sin x,\cos x\}$ and the $x$ -axis between $x=-\pi$ to $x=\pi$ be $A$ . Then $A^2$ …MediumNumerical value
9 Apr 2024, Shift 1 · Q9The parabola $y^2=4x$ divides the area of the circle $x^2+y^2=5$ in two parts. The area of the smaller part is equal to :MediumSingle correct
9 Apr 2024, Shift 2 · Q10The area (in square units) of the region enclosed by the ellipse $x^2+3y^2=18$ in the first quadrant below the line $y=x$ isMediumSingle correct
29 Jan 2024, Shift 1 · Q25The area (in sq. units) of the part of the circle $x^2+y^2=169$ which is below the line $5x-y=13$ is…HardNumerical value
30 Jan 2024, Shift 2 · Q26The area of the region enclosed by the parabola $(y-2)^2 = x - 1$ , the line $x - 2y + 4 = 0$ and the positive coordinate axes is ________.MediumNumerical value
31 Jan 2024, Shift 1 · Q10The area of the region $\left\{(x,y):y^2\leq4x,\ x<4,\ \frac{xy(x-1)(x-2)}{(x-3)(x-4)}>0,\ x\neq3\right\}$ isHardSingle 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
6 Apr 2023, Shift 1 · Q26If the area of the region $S=\{(x,y):2y-y^2\le x^2\le 2y,\ x\ge y\}$ is equal to $\frac{n+2}{n+1}-\frac{\pi}{n-1}$ , then the natural…HardNumerical value
8 Apr 2023, Shift 2 · Q27Let the area enclosed by the lines $x + y = 2$ , $y = 0$ , $x = 0$ and the curve $f(x) = \min\left\{x^2 + \frac{3}{4}, 1 + [x]\right\}$ …HardNumerical value
11 Apr 2023, Shift 1 · Q9Area of the region $\{(x,y) : x^2 + (y-2)^2 \le 4,\ x^2 \ge 2y\}$ isMediumSingle correct
13 Apr 2023, Shift 2 · Q11The area of the region $\{(x,y): x^2\le y\le |x^2-4|,\ y\ge1\}$ isHardSingle correct
25 Jul 2022, Shift 1 · Q8The area of the region given by $A=\{(x,y):x^2\le y\le\min\{x+2,\,4-3x\}\}$ is :MediumSingle correct
25 Jul 2022, Shift 1 · Q13Let the locus of the centre $(\alpha,\beta)$ , $\beta>0$ , of the circle which touches the circle $x^2+(y-1)^2=1$ externally and also…MediumSingle correct
24 Jun 2022, Shift 1 · Q29Let S be the region bounded by the curves $y=x^3$ and $y^2=x$ . The curve $y=2|x|$ divides S into two regions of areas $R_1$ and $R_2$ . If…HardNumerical value
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
25 Jul 2021, Shift 1 · Q63The area (in sq. units) of the region, given by the set $\{(x,y)\in\mathbf{R}\times\mathbf{R}\mid x\ge0,\ 2x^2\le y\le4-2x\}$ is :EasySingle correct
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
8 Jan 2020, Shift 1 · Q61For $a>0$ , let the curves $C_1: y^2=ax$ and $C_2: x^2=ay$ intersect at origin O and a point P. Let the line $x=b$ ( $0<b<a$ ) intersect 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
2 Sep 2020, Shift 1 · Q62Area (in sq. units) of the region outside $\frac{|x|}{2}+\frac{|y|}{3}=1$ and inside the ellipse $\frac{x^{2}}{4}+\frac{y^{2}}{9}=1$ is :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
2 Apr 2017 (offline) · Q76The area (in sq. units) of the region $\{(x,y):x\geq0,\ x+y\leq3,\ x^2\leq4y\ \text{and}\ y\leq1+\sqrt{x}\}$ is :HardSingle correct