Question

Find the area bounded by the curves $y=\sqrt{x},y=x$

Answer 1

$y=\sqrt{x}y=x\sqrt{x}=xx=x^{2}x=0,1$

The area is given as ${\int }_0^1\sqrt{x}-xdx{\int }_0^1\sqrt{x}dx-{\int }_0^{1}xdx{\frac{2x^{3/2}}{3}|}_0^1-{\frac{x^2}{2}|}_0^1\frac{2}{3}-\frac{1}{2}=\frac{1}{6}$