The value of the integral $\mathop \smallint \limits_0^{\pi /4} \,\,\frac{{\sin \,\,\theta \,\, + \,\,\cos \,\,\theta }}{{9\,\, + \,\,16\,\,\sin \,\,2\theta }}\,\,d\theta $, is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of the integral

\int \limits_0^{\pi /4} \,\,\frac{{\sin \,\,\theta \,\, + \,\,\cos \,\,\theta }}{{9\,\, + \,\,16\,\,\sin \,\,2\theta }}\,\,d\theta

, is

View answer and explanation

Correct option: C

\frac{1}{{20}}\,\,\log \,\,3

Option C (

\frac{1}{{20}}\\\,\log \\,3

) is correct because it is the value obtained after evaluating the definite integral using substitution.

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