What is the value of ∫[0 to 2π] cos³x dx?

What is the value of ∫[0 to 2π] cos³x dx?

• A. 1
• B. 4/3
• C. 0
• D. π

Answer: C) 0

Explanation: Using the property ∫[0 to 2a] f(x) dx = 0 if f(2a - x) = -f(x). We use ∫[0 to π] f(x) + ∫[π to 2π] f(x). Actually, f(x+π) = -f(x), so the integral over a full period of an odd power of cos x is 0.