The equations of curve y = √x and line y = x

Solving the equations y = √x ⇒ y² = x and y = x, we get

\[\begin{array}{*{35}{l}}

{{x}^{2}}~=\text{ }x  \\

{{x}^{2}}~-\text{ }x\text{ }=\text{ }0  \\

x\left( x\text{ }-\text{ }1 \right)\text{ }=\text{ }0  \\

So,\text{ }x\text{ }=\text{ }0,\text{ }1  \\

\end{array}\]

Now, the required area of the shaded region

Therefore, the required area = 1/6 sq.units.