Question

Solve:${\int }_0^{\pi /2}sinx{\cos }^{3}xdx$

Answer 1

${\int }_0^{\frac{\pi }{2}}\sin x{\cos }^{3}xdxLet\cos x=t\Rightarrow \sin xdx=-dtalso,atx=0;t=1andatx=\frac{\pi }{2};t=0\therefore {\int }_0^{\frac{\pi }{2}}\sin x{\cos }^{3}xdx=-{\int }_1^0{t}^{3}dt={-\left[\frac{t^4}{4}\right]}_1^0=\frac{1}{4}$