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Area Under The Curve - JEE Main Previous Year Question with Solutions

Practice JEE Main & Advanced Area Under the Curve previous year questions with detailed solutions to strengthen integration concepts, improve problem-solving skills, and boost exam preparation.

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Q. The area of the region bounded by the parabola $(\mathrm{y}-2)^{2}$ = x – 1, the tangent to the parabola at the point (2, 3) and the x–axis is :- (1) 9            (2) 12            (3) 3              (4) 6 [AIEEE-2009]
Ans. (1)
Q. The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 and x = $\frac{3 \pi}{2}$ is :- (1) $4 \sqrt{2}-2$ (2) $4 \sqrt{2}+2$ (3) $4 \sqrt{2}-1$ (4) $4 \sqrt{2}+1$ [AIEEE-2010]
Ans. (1)
Q. The area of the region enclosed by the curves $y=x, x=e, y=\frac{1}{x}$ and the positive $x$ -axis is:- (1) $\frac{3}{2}$ square units (2) $\frac{5}{2}$ square units (3) $\frac{1}{2}$ square units (4) 1 square units [AIEEE-2011]
Ans. (1)
Q. The area bounded by the curves $y^{2}=4 x$ and $x^{2}=4 y$ is :- (1) 0             (2) $\frac{32}{3}$              (3) $\frac{16}{3}$               (4) $\frac{8}{3}$ [AIEEE-2011]
Ans. (3)
Q. The area bounded between the parabolas $x^{2}=\frac{y}{4}$ and $x^{2}=9 y,$ and the straight line $y=2$ is : (1) $10 \sqrt{2}$ (2) $20 \sqrt{2}$ (3) $\frac{10 \sqrt{2}}{3}$ (4) $\frac{20 \sqrt{2}}{3}$ [AIEEE-2012]
Ans. (4)
Q. The area (in square units) bounded by the curves $y=\sqrt{x}, 2 y-x+3=0,$ x-axis and lying in the first quadrant is : (1) 9         (2) 36            (3) 18           (4) $\frac{27}{4}$ [JEE (Main)-2013]
Ans. (1)
Q. The area bounded by the curve y = ln(x) and the lines y = 0, y = ln (3) and x = 0 is equal to : (1) 3 ln (3) – 2                      (2) 3                    (3) 2                      (4) 3 ln (3) + 2 [JEE-Main (On line)-2013]
Ans. (3)
Q. The area of the region (in sq. units), in the first quadrant, bounded by the parabola y = $9 x^{2}$ and the lines x = 0, y = 1 and y = 4, is :- (1) 7/9             (2) 14/3              (3) 14/9              (4) 7/3 [JEE-Main (On line)-2013]
Ans. (3)
Q. The area under the curve $y=|\cos x-\sin x|, 0 \leq x \leq \frac{\pi}{2},$ and above $x$ -axis is : (1) $2 \sqrt{2}$ (2) $2 \sqrt{2}+2$ (3) 0 (4) $2 \sqrt{2}-2$ [JEE-Main (On line)-2013]
Ans. (4) Area $=2 \int_{0}^{\pi / 4}(\cos x-\sin x) d x=-2+2 \sqrt{2}$
Q. Let $f:[-2,3] \rightarrow[0, \infty)$ be a continuous function such that $f(1-x)=f(x)$ for all $x \in[-2,3] .$ If $R_{1}$ is the numerical value of the area of the region bounded by $y=f(x), x=-2, x=3$ and the axis of $x$ and $R_{2}=\int_{-2}^{3} x f(x) d x,$ then : (1) $2 \mathrm{R}_{1}=3 \mathrm{R}_{2}$ (2) $\mathrm{R}_{1}=\mathrm{R}_{2}$ (3) $3 \mathrm{R}_{1}=2 \mathrm{R}_{2}$ (4) $\mathrm{R}_{1}=2 \mathrm{R}_{2}$ [JEE-Main (On line)-2013]
Ans. (4)
Q. The area of the region described by $\mathrm{A}=\left\{(\mathrm{x}, \mathrm{y}): \mathrm{x}^{2}+\mathrm{y}^{2} \leq 1 \text { and } \mathrm{y}^{2} \leq 1-\mathrm{x}\right\}$ is : (1) $\frac{\pi}{2}+\frac{4}{3}$ (2) $\frac{\pi}{2}-\frac{4}{3}$ (3) $\frac{\pi}{2}-\frac{2}{3}$ (4) $\frac{\pi}{2}+\frac{2}{3}$ [JEE(Main)-2014]
Ans. (1)
Q. The area (in sq.units) of the region $\left\{(\mathrm{x}, \mathrm{y}): \mathrm{y}^{2} \geq 2 \mathrm{x} \text { and } \mathrm{x}^{2}+\mathrm{y}^{2} \leq 4 \mathrm{x}, \mathrm{x} \geq 0, \mathrm{y} \geq 0\right\}$ is :- (1) $\frac{\pi}{2}-\frac{2 \sqrt{2}}{3}$ (2) $\pi-\frac{4}{3}$ (3) $\pi-\frac{8}{3}$ (4) $\pi-\frac{4 \sqrt{2}}{3}$ [JEE(Main)-2016]
Ans. (3)
Q. The area (in sq. units) of the region $\left\{(\mathrm{x}, \mathrm{y}\}: \mathrm{x} \geq 0, \mathrm{x}+\mathrm{y} \leq 3, \mathrm{x}^{2} \leq 4 \mathrm{y} \text { and } \mathrm{y} \leq 1+\sqrt{\mathrm{x}}\right\}$ is : (1) $\frac{5}{2}$ (2) $\frac{59}{12}$ (3) $\frac{3}{2}$ (4) $\frac{7}{3}$ [JEE(Main)-2017]
Ans. (1)
Q. Let $g(x)=\cos x^{2}, f(x)=\sqrt{x}$ and $\alpha, \beta(\alpha<\beta)$ be the roots of the quadratic equation $18 x^{2}-9 \pi x+\pi^{2}=0 .$ Then the area (in sq. units) bounded by the curve $y=(\operatorname{gof})$ (x) and the lines $x=\alpha, x=\beta$ and $y=0$ is- ( 1)$\frac{1}{2}(\sqrt{3}+1)$ (2) $\frac{1}{2}(\sqrt{3}-\sqrt{2})$ (3) $\frac{1}{2}(\sqrt{2}-1)$ ( 4)$\frac{1}{2}(\sqrt{3}-1)$ [JEE (Main)-2018]
Ans. (4)

Frequently Asked Questions

Find answers to common questions.

How much weightage does Area Under The Curve carry in JEE Main?

Area Under The Curve typically contributes 1–2 questions per JEE Main paper, worth 4–8 marks. Over the past decade, it has appeared in nearly every session. It is part of the Integral Calculus unit, which collectively carries approximately 10–15% of the JEE Main Mathematics paper, making it one of the higher-weightage units to prioritise.


Is Area Under the Curve difficult in JEE Main?

The difficulty is moderate to hard. The calculation itself is straightforward if you set up the problem correctly. The real challenge is correctly identifying boundaries, finding intersection points, and deciding the direction of integration. Students who practise 20–30 previous year questions from this chapter consistently report it becoming one of their scoring topics.

What type of curves appear most frequently in Area Under Curve JEE Main questions?

Parabolas (both $x = f(y)$ and $y = f(x)$ forms), trigonometric curves ($\sin x$ and $\cos x$), logarithmic curves, and circles are the most frequent. Many questions combine two or three of these into a composite bounded region — for example, a circle intersecting a parabola, as seen in the 2014 and 2016 questions.

Should I integrate with respect to x or y in JEE Main area problems?

Choose based on which gives simpler limits and integrand. For parabolas of the form $(y - k)^2 = x - h$, integrating with respect to $y$ is almost always cleaner. For most other curves, $dx$ integration with vertical strips works well. Practising both orientations on the same problem builds the intuition to choose quickly under exam pressure.

Which Class 12 NCERT exercises are most relevant for this topic?

Chapter 8 (Application of Integrals) in Class 12 NCERT is directly relevant. Work through all examples and Exercise 8.1 and 8.2 completely. The miscellaneous exercise at the end of Chapter 8 contains problems at near-JEE level. You can find complete worked solutions at NCERT Solutions for Class 12 Maths.

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fnfOzvSR
March 30, 2026, 3:09 a.m.
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fnfOzvSR
March 30, 2026, 3:09 a.m.
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fnfOzvSR
March 30, 2026, 3:07 a.m.
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fnfOzvSR
March 30, 2026, 3:07 a.m.
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mia khalifa
March 23, 2022, 9:36 p.m.
very helpful .... but solution must be needed for better performance
akshat physics wallah
Feb. 23, 2022, 11:05 p.m.
include 2022 Q also
student
May 14, 2021, 8:16 a.m.
really helps revising
D rugved
April 4, 2021, 8:54 p.m.
tq
nikhil
March 11, 2021, 6:55 p.m.
thanku
G.Lakshmi
March 11, 2021, 5:37 p.m.
Nice.....its very useful
Devika mourya
Dec. 18, 2020, 2:51 p.m.
It's very helpful
Pawan kumar
Oct. 2, 2020, 4:02 p.m.
Math
Rahul Rathore
Feb. 20, 2020, 12:20 p.m.
Is page per previous year question paper ke solution kyon nahin hai
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