∫₀^π x sin x cos² x dx equals:

∫₀^π x sin x cos² x dx equals:

• A. π/3
• B. 2π/3
• C. π/6
• D. π/2

Answer: A) π/3

Explanation: Use property: ∫₀^π x f(sin x) dx = (π/2) ∫₀^π f(sin x) dx. Here f(sin x) = sin x cos² x = sin x (1 − sin² x) = sin x − sin³ x. So I = (π/2) ∫₀^π (sin x − sin³ x) dx. ∫₀^π sin x dx = 2. ∫₀^π sin³ x dx = 4/3. So (π/2)(2 − 4/3) = (π/2)(2/3) = π/3.