COMEDK · Maths · 30. Definite Integration
\(\int_{0}^{\pi / 2} \log (\tan x) d x=\)
- A \(\frac{\pi}{2}\)
- B 0
- C 1
- D \(\frac{\pi}{4}\)
Answer & Solution
Correct Answer
(B) 0
Step-by-step Solution
Detailed explanation
Let \(\quad I=\int_{0}^{\pi / 2} \log (\tan x) d x\) \(\Rightarrow \quad I=\int_{0}^{\pi / 2} \log \tan \left(\frac{\pi}{2}-x\right) d x\) \(\Rightarrow \quad I=\int_{0}^{\pi / 2} \log \cot x d x\) \(\Rightarrow \quad I=\int_{0}^{\pi / 2} \log \frac{1}{\tan x} d x\)…
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