JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

The value of the integral

I=\int\limits_{0}^a \frac{x^4}{\left(a^2+x^2\right)^4} d x

, is

View answer and explanation

Correct option: A

\frac{1}{16 a^3}\left(\frac{\pi}{4}-\frac{1}{3}\right)

Option A (

\frac{1}{16 a^3}(\frac{\pi}{4}-\frac{1}{3})

) is correct because it is obtained by using trigonometric substitution and simplifying the integral.

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