$\mathop \smallint \limits_0^{\pi /2} \,\,\frac{{{{\sin }^2}\,\,x}}{{\sin \,\,x\,\, + \,\,\cos \,\,x}}\,\,dx$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

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

is equal to

View answer and explanation

Correct option: C

\frac{1}{{\sqrt 2 }}\,\,\log \,\,\left( {\sqrt 2 + 1} \right)

Option C (

\frac{1}{{\sqrt 2 }}\,\,\log \,\,\left( {\sqrt 2 + 1} \right)

) is correct because using the property of definite integrals and simplifying leads to the given answer.

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