JEE MAIN - Mathematics (2022 - 25th June Evening Shift - No. 6)
The area of the region enclosed between the parabolas y2 = 2x $$-$$ 1 and y2 = 4x $$-$$ 3 is
$${1 \over {3}}$$
$${1 \over {6}}$$
$${2 \over {3}}$$
$${3 \over {4}}$$
Explanation
Area of the shaded region
_25th_June_Evening_Shift_en_6_1.png)
$$ = 2\int_0^1 {\left( {{{{y^2} + 3} \over 4} - {{{y^2} + 1} \over 2}} \right)dy} $$
$$ = 2\int_0^1 {\left( {{1 \over 4} - {{{y^2}} \over 4}} \right)dy} $$
$$ = 2\left[ {{1 \over 4} - {1 \over {12}}} \right] = {1 \over 3}$$
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