$\mathop \smallint \nolimits_0^{\pi /4} \,\,\log \,\,(1 + \tan \,\,x)\,\,dx$ is equal to

$\frac{\pi }{4}\,\,{\log _2}\,\,e$

$\frac{\pi }{4}\,\,{\log _e}\,\,2$

$\frac{\pi }{8}\,\,{\log _e}\,\,\left( {\frac{1}{2}} \right)$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

\int \nolimits_0^{\pi /4} \,\,\log \,\,(1 + \tan \,\,x)\,\,dx

is equal to

View answer and explanation

Correct option: A

\frac{\pi }{8}\,\,{\log _e}\,\,2

Option A is correct because the integral is solved by using properties of definite integrals and logarithmic functions.

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