Wallis' Formula: $I_n$ = integral$\frac{0 to pi}{2}$ $sin^n$ x dx = integral$\frac{0 to pi}{2}$ $cos^n$ x dx

$I_n$ = [$\frac{n-1}{n}$] * [$\frac{n-3}{(n-2)}$] * ... * $\frac{pi}{2 or 1}$

• Last factor is pi/2 if n is even (sequence ends at 1/2 * pi/2)
• Last factor is 1 if n is odd $\frac{sequence ends at 2}{3 * 1}$

Quick Values: $I_0$ = pi/2, $I_1$ = 1, $I_2$ = pi/4, $I_3$ = 2/3, $I_4$ = 3pi/16, $I_5$ = 8/15, $I_6$ = 5pi/32

Extended Wallis: integral(0 to pi) $sin^n$ x dx = 2 * $I_n$ (even function on [0, pi] after King's Rule) integral(0 to 2pi) $sin^n$ x dx = 4 * $I_n$ (when n is even), 0 (when n is odd)