QJEEM22Ma6741: JEE Main 2022 Mathematics - Class 12 JEEM22Ma6741 Solution: The area of the region S = {(x, y) : y 2 ≤ 8x, y ≥ 2 x, x ≥ 1} is

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The area of the region S = {(x, y) : y² $\leq$ 8x, y $\geq$ $\sqrt{2}$ x, x $\geq$ 1} is

Accepted Answer

JEE Main 2022 (Online) 28th June Morning Shift Mathematics - Area Under The Curves Question 77 English Explanation

Required area

$= \int_{1}^{4} (\sqrt{8 x} - \sqrt{2} x) d x$

$= {\frac{2 \sqrt{8}}{3} x^{\frac{3}{2}} - \frac{x^{2}}{\sqrt{2}} |}_{1}^{4}$

$= \frac{16 \sqrt{3}}{3} - \frac{16}{\sqrt{2}} - \frac{2 \sqrt{8}}{3} + \frac{1}{\sqrt{2}}$

$= \frac{11 \sqrt{2}}{6}$ sq. units

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