NIMCET 2018 Question Paper with solutions

The intersecting point of given curve is given by
${\mathit{x}}^2$ = x
⇒ ${\mathit{x}}^2$ - x = 0
⇒ x (x - 1) = 0
⇒ x = 0 , 1
⇒ y = 0 , 1
∴ Point of intersection are (0, 0) and (1, 1).
∴ Required area = $\underset{0}{\overset{1}{\int }}$ ($\sqrt{\mathit{x}}$ - x) dx = ${\left[\frac{{\mathit{x}}_2^3}{\frac{3}{2}}-\frac{{\mathit{x}}^2}{2}\right]}_0^1$
= $\frac{2}{3}-\frac{1}{2}$ = $\frac{1}{6}$ sq . units