Area Under The Curve – JEE Main Previous Year Question with Solutions
JEE Main Previous Year Question of Math with Solutions are available at eSaral. Practicing JEE Main Previous Year Papers Questions of mathematics will help the JEE aspirants in realizing the question pattern as well as help in analyzing weak & strong areas. Get detailed Class 11th &12th Physics Notes to prepare for Boards as well as competitive exams like IIT JEE, NEET etc. eSaral helps the students in clearing and understanding each topic in a better way. eSaral is providing complete chapter-wise notes of Class 11th and 12th both for all subjects. Besides this, eSaral also offers NCERT Solutions, Previous year questions for JEE Main and Advance, Practice questions, Test Series for JEE Main, JEE Advanced and NEET, Important questions of Physics, Chemistry, Math, and Biology and many more. Download eSaral app for free study material and video tutorials.
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]

Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...

Sol. (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]

Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...

Sol. (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]

Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...

Sol. (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]

Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...

Sol. (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]

Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...

Sol. (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]

Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...

Sol. (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]

Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...

Sol. (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]

Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...

Sol. (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]

Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...

Sol. (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]

Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...

Sol. (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]

Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...

Sol. (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]

Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...

Sol. (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]

Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...

Sol. (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]

Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...

Sol. (4)  • May 14, 2021 at 8:16 am

really helps revising

0
• May 15, 2021 at 9:00 am

Excellent work bro

0
• April 4, 2021 at 8:54 pm

tq

74
• March 11, 2021 at 6:55 pm

thanku

2
• March 11, 2021 at 5:37 pm

Nice…..its very useful

0
• December 18, 2020 at 2:51 pm