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JEE Main 202124 FebruaryEvening Shift

Exam: JEE Main
Year: 2021
Date: 24 February
Shift: Evening Shift
Subject: Mathematics
Chapter: Area Under Curves

JEE Main 2021 · 24 February · Evening Shift · Mathematics · Area Under Curves

The area of the region: R = \ (x, y): 5 x ^ 2 ≤ y ≤ 2 x ^ 2 + 9\ is

The area of the region:

R = \left\{\left(x, y\right): 5{x}^{2} \le y \le 2{x}^{2} + 9\right\}

is $The area of the region: R = \ (x, y): 5 x ^ 2 ≤ y ≤ 2 x ^ 2 + 9\ is$

Options

A $9\sqrt{3}$ square units
B $12\sqrt{3}$ square units
C $11\sqrt{3}$ square units
D $6\sqrt{3}$ square units

Correct answer

B. $12\sqrt{3}$ square units

Step-by-step solution

$The area of the region: R = \ (x, y): 5 x ^ 2 ≤ y ≤ 2 x ^ 2 + 9\ is$

Required area $= 2{∫}_{0}^{\sqrt{3}}\left(2{x}^{2} + 9 - 5{x}^{2}\right)dx$

$= 2{\left[9x - {x}^{3}\right]}_{0}^{\sqrt{3}}$

$= 2\left[9\sqrt{3} - 3\sqrt{3}\right] = 12\sqrt{3}$ square units

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