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JEE Main 202227 JulyEvening Shift

Exam: JEE Main
Year: 2022
Date: 27 July
Shift: Evening Shift
Subject: Mathematics
Chapter: Area Under Curves

JEE Main 2022 · 27 July · Evening Shift · Mathematics · Area Under Curves

The area of the region enclosed by y ≤ 4 x ^ 2 , x ^ 2 ≤ 9y and y ≤...

The area of the region enclosed by

y \le 4{x}^{2}, {x}^{2} \le 9y

and

y \le 4

, is equal to The area of the region enclosed by y ≤ 4 x ^ 2 , x ^ 2 ≤ 9y and y ≤ 4 , is equal to

The area of the region enclosed by y ≤ 4 x ^ 2 , x ^ 2 ≤ 9y and y ≤ 4 , is equal to

Options

A $\dfrac{40}{3}$
B $\dfrac{56}{3}$
C $\dfrac{112}{3}$
D $\dfrac{80}{3}$

Correct answer

D. $\dfrac{80}{3}$

Step-by-step solution

Plotting the required region
Enclosed area $= 2{∫}_{0}^{4}\left(3\sqrt{y} - \dfrac{\sqrt{y}}{2}\right)dy$
$= 2{∫}_{0}^{4}\dfrac{5\sqrt{y}}{2}dy$
$= 5{\left[\dfrac{2}{3}y\dfrac{3}{2}\right]}_{0}^{4}$
$= \dfrac{10}{3} ( 4) \dfrac{3}{2} = \dfrac{80}{3}$

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