JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of the definite integral

\int\limits_{{-(\pi / 2)}}^{\pi / 2} \frac{\cos ^2 x}{1+5^x}

equals to:

View answer and explanation

Correct option: D

\frac{\pi}{4}

Option D (

\frac{\pi}{4}

) is correct because using the property

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

, the integral simplifies to

\int_0^{\pi/2} \cos^2 x dx = \frac{\pi}{4}

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