# Integrate : $\int \limits_0^{\large\frac{z}{2}}$$\cos x \sin ^3 x dx $\begin {array} {1 1} (a)\;\frac{z}{2} \\ (b)\;\frac{z}{4} \\ (c)\;\frac{1}{4} \\ (d)\;\frac{1}{2} \end {array}$ ## 1 Answer In that m=3,n=1 so formula will not apply directly, \sin x =t=> \cos x dx =dt at x=0,t=0 x = \large\frac{z}{2}$$,t=1$
$\int \limits_0^1 t^3. dt$
$=\bigg[\large\frac{t^4}{4} \bigg]_0^1$