The value of ∫₀¹ log(1/x − 1) dx is:
The value of ∫₀¹ log(1/x − 1) dx is:
- A. 0
- B. 1
- C. −1
- D. 2
Answer: A) 0
Explanation: I = ∫₀¹ log((1−x)/x) dx = ∫₀¹ log(1−x) dx − ∫₀¹ log x dx. By property ∫₀ᵃ f(x)dx = ∫₀ᵃ f(a−x)dx, ∫₀¹ log(1−x) dx = ∫₀¹ log x dx. So I = 0.
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