Chapter 8.4, Problem 50E

To determine

Whether the statement “If $x=\sin \theta$, then ${\displaystyle \underset{-1}{\overset{1}{\int }}{x}^2\sqrt{1-x^2}}dx=2{\displaystyle \underset{0}{\overset{\frac{\pi }{2}}{\int }}{\sin }^2}\theta {\cos }^2\theta$” is true or false.