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Question: Value of <img src="https://cdn.pureessence.tech/canvas_127.png?top_left_x=339&top_left_y=1647&width=...

Value of -

A

1

B

0

C

3

D

None of these

Answer

0

Explanation

Solution

take x = tanq

̃ ∫0π/2sin⁡θ⋅cos⁡θ⋅log⁡tan⁡θdθ\int _ { 0 } ^ { \pi / 2 } \sin \theta \cdot \cos \theta \cdot \log \tan \theta d \theta

I = ∫0n/2sin⁡θ⋅cos⁡θ⋅log⁡cot⁡θdθ\int _ { 0 } ^ { \mathrm { n } / 2 } \sin \theta \cdot \cos \theta \cdot \log \cot \theta \mathrm { d } \theta

2I = 0 ̃ I = 0