Mathematics

# If $\displaystyle\int_{0}^{\pi } \ln \sin x dx =k$, then the value of $\displaystyle\int_{0}^{\pi /4} \ln (1+\tan x) dx$ is:

$-\dfrac{k}{4}$

##### SOLUTION

Since
$\int_0^\pi \ln \sin x dx=-\dfrac{\pi}{2}\ln 2=k$
Hence:
$\int_0^{\pi/4} \ln (1+\tan x)dx=\dfrac{\pi}{8}\ln 2=-\dfrac k4$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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