Wallis' Formula: I_n = integral(0 to pi/2) sin^n x dx = integral(0 to pi/2) cos^n x dx

I_n = [(n-1)/n] * [(n-3)/(n-2)] * ... * (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 (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)