JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

\int \limits_{ - \pi /3}^{\pi /3} \,\,\left( {\frac{a}{3}\,\,\left| {\tan x} \right|\,\, + \,\,\frac{{b\,\,\tan \,\,x}}{{1 + \,\,\sec \,\,x}}} \right)\,\,dx = 0

where

a,\;\,\,b,\;\,\,c

are constants, then

c =

View answer and explanation

Correct option: C

- \,\,\frac{a}{\pi }\,\,\ln \,\,2

Option C (

- \,\frac{a}{\pi }\\,\ln \\,2

) is correct because after evaluating the definite integral and using properties of even and odd functions, we find that

c = - \\,\frac{a}{\pi }\\,\ln \\,2

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