QJEEM22Mab099: JEE Main 2022 Mathematics - Class 12 JEEM22Mab099 Solution: The area of the region bounded by y 2 = 8x and y 2 = 16(3 − x)…

Question

Verified Solution • 2025–26 Session moderate

The area of the region bounded by y² = 8x and y² = 16(3 $-$ x) is equal to:

Accepted Answer

$c_{1} : y^{2} = 8 x$

$c_{2} : y^{2} = 16 (3 - x)$

JEE Main 2022 (Online) 26th June Evening Shift Mathematics - Area Under The Curves Question 73 English Explanation

Solving c₁ and c₂

$48 - 16 x = 8 x$

$x = 2$

$∴$ $y = \pm 4$

$∴$ Area of shaded region

$= 2 \int_{0}^{4} {(\frac{48 - y^{2}}{16}) - (\frac{y^{2}}{8})} d y$

$= \frac{1}{8} {[48 y - y^{3}]}_{0}^{4} = 16$

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