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Area between Two Curves

Area bounded ...

Question

Area bounded by curves $y^{2} = x$ and $y = | x |$ is given by

A

\frac{1}{6}

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B

\frac{2}{3}

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C

- \frac{1}{6}

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D

\frac{1}{3}

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Solution

The correct option is D $\frac{1}{6}$
Solving $\sqrt{x} = x$
We get $x = 0, x = 1$
$A = \int_{0}^{1} (\sqrt{x} - x) d x$
$= {⎛ ⎝ \frac{x^{3 / 2}}{\frac{3}{2}} - \frac{x^{2}}{2} ⎞ ⎠}_{0}^{1} = \frac{2}{3} - \frac{1}{2} = \frac{1}{6}$

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