$\mathop \smallint \nolimits_0^{\pi /2} \frac{{\cos \,\,x - \sin \,\,x}}{{1 + \,\,\cos \,\,x\,\,\sin \,\,x}}\,\,dx$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \nolimits_0^{\pi /2} \frac{{\cos \,\,x - \sin \,\,x}}{{1 + \,\,\cos \,\,x\,\,\sin \,\,x}}\,\,dx

is equal to

View answer and explanation

Correct option: A

\mathrm{0}

Option A (

\mathrm{0}

) is correct because using the property of definite integrals

\int_0^a f(x) dx = \int_0^a f(a-x) dx

leads to the integral being equal to its negative.

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