The value of $\mathop \smallint \limits_{\pi /4}^{3\pi /4} \,\,\frac{x}{{1\,\, + \,\,\sin \,\,x}}\,\,dx$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Analyzing +4 | -1

The value of

\int \limits_{\pi /4}^{3\pi /4} \,\,\frac{x}{{1\,\, + \,\,\sin \,\,x}}\,\,dx

is equal to

View answer and explanation

Correct option: A

\left( {\sqrt 2 - 1} \right)\pi

Option A ((

\sqrt 2 - 1)\pi

) is correct because the integral can be solved by using the property

\int_a^b f(x) dx = \int_a^b f(a+b-x) dx

and then simplifying the resulting expression.

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