Calculus

Using Wallis' formula: $\int_0^{\pi/2} \sin^m(x) \cos^n(x) dx = \frac{(m-1)(m-3)\dots (n-1)(n-3)\dots}{(m+n)(m+n-2)\dots} \times \frac{\pi}{2}$ (when both $m, n$ are even). Here $m=4, n=2$: $I = \frac{(3)(1) \times (1)}{(6)(4)(2)} \times \frac{\pi}{2} = \frac{3}{48} \times \frac{\pi}{2} = \frac{1}{16} \times \frac{\pi}{2} = \frac{\pi}{32}$. Hence $k = 32$.