Evaluate ∫₀^π dx/(1 + sin x).

Evaluate ∫₀^π dx/(1 + sin x).

• A. 0
• B. 1
• C. 2
• D. π

Answer: C) 2

Explanation: ∫₀^π dx/(1+sin x). Multiply numerator and denominator by (1−sin x): = ∫₀^π (1−sin x)/cos² x dx = ∫₀^π (sec² x − sec x tan x) dx = [tan x − sec x]₀^π. At π: tan π = 0, sec π = −1 → 0 − (−1) = 1. At 0: tan 0 = 0, sec 0 = 1 → 0 − 1 = −1. So 1 − (−1) = 2.