AP EAMCET · Maths · Definite Integration
\(\int_0^{\pi / 2} \log |\tan x+\cot x| d x=\)
- A \(\pi \log 2\)
- B \(-\pi \log 2\)
- C \(\frac{\pi}{2} \log 2\)
- D \(2\pi \log 2\)
Answer & Solution
Correct Answer
(A) \(\pi \log 2\)
Step-by-step Solution
Detailed explanation
\(\int_0^{\pi / 2} \log |\tan x+\cot x| d x = \int_0^{\pi / 2} \log \left(\frac{1}{\sin x \cos x}\right) d x = \int_0^{\pi / 2} \log \left(\frac{2}{\sin 2x}\right) d x\) \(= \int_0^{\pi / 2} \log 2 d x - \int_0^{\pi / 2} \log (\sin 2x) d x\)…
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