# The area enclosed between the curves $\dpi{100} y^{2}=x\; and\; y=\left | x \right |\; is$ Option 1) 1/6 Option 2) 1/3 Option 3) 2/3 Option 4) 1

P Prateek Shrivastava

As we learnt in

Area along y axis -

Let $y_{1}= f_{1}(x)\, and \, y_{2}= f_{2}(x)$ be two curve, then area bounded by the curves and the lines

y = a and y = b is

$A=\int_{a}^{b}\left ( x_{2}-x_{1} \right )dy$

- wherein

$Area= \int_{0}^{1}\left ( \sqrt{x}-x \right )dx$

$= \left [ \frac{2x^{3/2}}{3}- \frac{x^2}{2} \right ]_{0}^{1}$

$= \frac{2}{3}- \frac{1}{2}= \frac{1}{6}$

Option 1)

1/6

Correct

Option 2)

1/3

Incorrect

Option 3)

2/3

Incorrect

Option 4)

1

Incorrect

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