∫₀^(π/2) dx/(1 + tan x) equals:

∫₀^(π/2) dx/(1 + tan x) equals:

• A. π/2
• B. π/4
• C. π/8
• D. π

Answer: B) π/4

Explanation: I = ∫₀^(π/2) dx/(1 + tan x) = ∫₀^(π/2) cos x/(cos x + sin x) dx. Using property ∫₀ᵃ f(x)dx = ∫₀ᵃ f(a−x)dx. I = ∫₀^(π/2) cos(π/2−x)/(cos(π/2−x)+sin(π/2−x)) dx = ∫₀^(π/2) sin x/(sin x+cos x) dx. Adding: 2I = ∫₀^(π/2) (cos x+sin x)/(cos x+sin x) dx = π/2. So I = π/4.