The value $\left( {\rm{s}} \right)$ of $\mathop \smallint \nolimits_0^1 \,\,\frac{{{x^4}{{\left( {1 - x} \right)}^4}}}{{1 + {x^2}}}\,\,dx$ is (are)

$\frac{{71}}{{15}}\,\, - \,\,\frac{{3\,\pi }}{2}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Analyzing +4 | -1

The value

\left( \mathrm{s} \right)

\int \nolimits_0^1 \,\,\frac{{{x^4}{{\left( {1 - x} \right)}^4}}}{{1 + {x^2}}}\,\,dx

is (are)

View answer and explanation

Correct option: A

\frac{{22}}{7}\,\, - \,\,\pi

Option A

\frac{{22}}{{7}}\, - \,\pi

is correct because after expanding and integrating the given expression, the result simplifies to

\frac{22}{7} - \pi

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