QJEEM07Maafc9: JEE Main 2007 Mathematics - Class 12 JEEM07Maafc9 Solution: The area enclosed between the curves and is :

Question

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The area enclosed between the curves

{y^2} = x

and

y = \left| x \right|

is :

Accepted Answer

The area enclosed between the curves

{y^2} = x

and

y = \left| x \right|

From the figure, area lies between

{y^2} = x

and

y = x

\therefore

Required area

= \int_0^1 {\left( {{y_2} - {y_1}} \right)} dx

= \int_0^1 {\left( {\sqrt x - x} \right)dx = \left[ {{{{x^{3/2}}} \over {3/2}} - {{{x^2}} \over 2}} \right]} _0^1

\therefore

Required area

= {2 \over 3}\left[ {{x^{3/2}}} \right]_0^1 - {1 \over 2}\left[ {{x^2}} \right]_0^1

= {2 \over 3} - {1 \over 2} = {1 \over 6}

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