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Vector Component

Area bounded ...

Question

Area bounded by the curve $x y^{2} = a^{2} (a - x)$ and $Y$ -axis is

A

π

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B

\frac{π}{2}

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C

\frac{π a^{2}}{2}

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D

π a^{2}

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Solution

The correct option is D $π a^{2}$
$x y^{2} = a^{2} (a - x)$
$x = \frac{a^{3}}{y^{2} + a^{2}}$
$\int x d y = \int \frac{a^{3}}{y^{2} + a^{2}} d y$ from $- \infty$ to $\infty$
$A r e a = a^{2} t a n^{- 1} (\frac{y}{a}) |_{- \infty}^{\infty}$
$A r e a = π a^{2}$

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