Let I m = /2 0 sin m x dx. (a) Show that I 0 = /2 and I 1 = 1. (b) Prove

Let I_m = ∫^π/2₀ sin^m x dx.
(a) Show that I₀ = π/2 and I₁ = 1.
(b) Prove that, for m ≥ 2,

(c) Use (a) and (b) to compute I_m for m = 2, 3, 4, 5.

Im = m-1 m -Im-2