The area enclosed between the curves y^2=x and y=|x| is:

Question

The area enclosed between the curves $y^2=x$ and $y=|x|$ 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 $$ = {2 \over 3}\left[ {{x^{3/2}}} \right]_0^1 - {1 \over 2}\left[ {{x^2}} \right]_0^1$$

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

Solutions · 1