\[\mathop \smallint \nolimits_2^{\pi /2} \,\,\frac{{\cos \,\,x}}{{(1\,\, + \,\,\sin \,\,x)\,\,(2\,\, + \,\,\sin \,\,x)}}\;\,\,dx\] is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

\int \nolimits_2^{\pi /2} \,\,\frac{{\cos \,\,x}}{{(1\,\, + \,\,\sin \,\,x)\,\,(2\,\, + \,\,\sin \,\,x)}}\;\,\,dx

is equal to

View answer and explanation

Correct option: A

\log \,\,\frac{4}{3}

Option A (

\log \,\frac{4}{3}

) is correct because after substitution and partial fraction decomposition, the definite integral evaluates to this value.

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