Chapter 7.2, Problem 69E

To determine

(a)

To show $I_0=\frac{\pi }{2}\&I_1=1$, where

$I_m={\displaystyle \underset{0}{\overset{\pi /2}{\int }}{\sin }^{m}xdx}$

To determine

(b)

To prove for $m\ge 2$,

$I_m=\frac{m-1}{m}{I}_{m-2}$, where

$I_m={\displaystyle \underset{0}{\overset{\pi /2}{\int }}{\sin }^{m}xdx}$

To determine

(c)

To compute $I_m$ for $m=2,3,4,5$