QJEEM22Ma6586: JEE Main 2022 Mathematics - Class 12 JEEM22Ma6586 Solution: The area of the region enclosed between the parabolas y 2 = 2x…

Question

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The area of the region enclosed between the parabolas y² = 2x $-$ 1 and y² = 4x $-$ 3 is

Accepted Answer

Area of the shaded region

JEE Main 2022 (Online) 25th June Evening Shift Mathematics - Area Under The Curves Question 72 English Explanation

$= 2\int_0^1 {\left( {{{{y^2} + 3} \over 4} - {{{y^2} + 1} \over 2}} \right)dy}$

$= 2\int_0^1 {\left( {{1 \over 4} - {{{y^2}} \over 4}} \right)dy}$

$= 2\left[ {{1 \over 4} - {1 \over {12}}} \right] = {1 \over 3}$

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