The area enclosed between the curves y^{2}=x\; and\; y=\left | x \right |\; is

  • Option 1)

    1/6

  • Option 2)

    1/3

  • Option 3)

    2/3

  • Option 4)

    1

 

Answers (1)

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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