∫₀^π cos⁷ x dx equals:

∫₀^π cos⁷ x dx equals:

• A. 0
• B. 1
• C. 2
• D. π

Answer: A) 0

Explanation: cos⁷ x is odd about π/2? Actually cos x is negative in [π/2, π], odd power retains sign. But ∫₀^π cos⁷ x dx = 0 by symmetry because cos(π−x) = −cos x, so cos⁷(π−x) = −cos⁷ x. Integral from 0 to π/2 cancels with π/2 to π.