$\mathop \smallint \nolimits_0^1 \,\,\frac{{{x^3}\;\,dx}}{{{{\left( {{x^2}\,\, + \,\,1} \right)}^{3/2}}}}$ is equal to

${\left( {\sqrt 2 - 1} \right)^2}$

$\frac{{{{\left( {\sqrt 2 - 1} \right)}^2}}}{2}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

\int \nolimits_0^1 \,\,\frac{{{x^3}\;\,dx}}{{{{\left( {{x^2}\,\, + \,\,1} \right)}^{3/2}}}}

is equal to

View answer and explanation

Correct option: D

None of these

Option D (None of these) is correct because the calculated value of the integral

\int \nolimits_0^1 \,\,\frac{{{x^3}\,dx}}{{{{\left( {{x^2}\,\,+\,1} \right)}^{3/2}}}}

does not match any of the given options.

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