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Q.

The area of the region bounded by the parabola $y^{2} = 4 x$ and $x^{2} = 4 y$ is

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a

$\frac{8}{3}$

b

$\frac{16}{3}$

c

$\frac{4}{3}$

d

$\frac{32}{2}$

answer is C.

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Detailed Solution

$y^{2} = 4 x, x^{2} = 4 y$

Question Image

$A = \int_{0}^{4} (2 \sqrt{x} - \frac{x^{2}}{4}) d x = 2. \frac{2}{3} {(x^{3 / 2})}_{0}^{4} - \frac{1}{12} {(x^{3})}_{0}^{4}$

$= \frac{4}{3} (8) - \frac{1}{12} (4^{3}) = \frac{32}{3} - \frac{16}{3} = \frac{16}{3}$

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The area of the region bounded by the parabola y2=4x and x2=4y is