The value of $\mathop \smallint \nolimits_0^1 \,\,\frac{{{x^4} + \,\,1}}{{{x^2} + \,\,1}}\,\,dx$ is

$\frac{1}{6}\,\,\left( {3\,\, - \,\,4\pi } \right)$

$\frac{1}{6}\,\,\left( {3\,\, + \,\,4\,\pi } \right)$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

The value of

\int \nolimits_0^1 \,\,\frac{{{x^4} + \,\,1}}{{{x^2} + \,\,1}}\,\,dx

View answer and explanation

Correct option: D

\frac{1}{6}\,\,\left( {3\pi \,\, - \,\,4\,} \right)

Option D (

\frac{1}{6}\\,,\left( {3\pi \\, - \\,4\} \right)

) is correct because after dividing and integrating, the result is

\frac{1}{6}\\,,\left( {3\pi \\, - \\,4\} \right)

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