Question:

Put $2x = t \Rightarrow 2dx = dt \Rightarrow dx = \frac{dt}{2}$<br>When $x = 0, t = 0$; when $x = \pi/4, t = \pi/2$<br>$I = \int_{0}^{\pi/2} \sin^5 t \frac{dt}{2} = \frac{1}{2} \int_{0}^{\pi/2} \sin^5 t \, dt$<br>Using Walli's Theorem for $n = 5$ (odd):<br>$I = \frac{1}{2} \left[ \frac{4 \cdot 2 \cdot 1}{5 \cdot 3 \cdot 1} \right] = \frac{1}{2} \cdot \frac{8}{15} = \frac{4}{15}$