∫0π/2 sin⁡2xlog⁡tan⁡xdx is equal to - Infinity Learn by Sri Chaitanya

A
$π$
B
$\frac{π}{2}$
C
0
D
1

Solution:

Let $I = \int_{0}^{π / 2} \sin 2 x \log \tan x d x$

Then,

$\begin{array}{l} I \int_{0}^{π / 2} \sin 2 (\frac{π}{2} - x) \log \tan (\frac{π}{2} - x) d x \\ \Rightarrow I = \int_{0}^{π / 2} \sin 2 x \log \cot x d x \end{array}$

Adding (i) and (ii), we get

$\begin{array}{l} 2 I = \int_{0}^{π / 2} \sin 2 x (\log \tan x + \log \cot x) d x \\ \Rightarrow 2 I = \int_{0}^{π / 2} \sin 2 x \times \log 1 d x \Rightarrow 2 I = 0 \Rightarrow I = 0 \end{array}$

$\int_{0}^{π / 2} \sin 2 x \log \tan x d x$ is equal to

Solution:

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