Evaluate ∫[0 to π/2] ln(tan x) dx.
Evaluate ∫[0 to π/2] ln(tan x) dx.
- A. π/2
- B. π/4
- C. 0
- D. 1
Answer: C) 0
Explanation: Let I = ∫[0 to π/2] ln(tan x) dx. Using property ∫ f(x) = ∫ f(a-x), I = ∫ ln(cot x) dx = - ∫ ln(tan x) dx = -I. Thus, 2I = 0, so I = 0.
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