The value of $\mathop \smallint \limits_0^{\pi /2} \frac{1}{{9\,\,\cos \,\,x + 12\,\,\sin \,\,x}}\,\,dx$, is

$\frac{1}{{15}}\,\,{\log _{10}}\,\,6$

$\log \,\,\left( {\frac{6}{{15}}} \right)$

$\log \,\,\left( {\frac{{15}}{6}} \right)$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of

\int \limits_0^{\pi /2} \frac{1}{{9\,\,\cos \,\,x + 12\,\,\sin \,\,x}}\,\,dx

, is

View answer and explanation

Correct option: B

\frac{1}{{15}}\,\,{\log _e}\,\,6

Option B (

\frac{{1}}{{15}}\,{\log _e}\,6

) is correct because it is the result of evaluating the definite integral using trigonometric substitution and logarithmic properties.

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