If ${I_1} = \mathop \smallint \limits_0^\infty \,\,\frac{1}{{1 + {x^4}}}\,\,dx$ and ${I_2} = \mathop \smallint \limits_0^\infty \,\,\frac{{{x^2}}}{{1\,\, + \,\,{x^4}}}\,\,dx$. Then $\frac{{{I_1}}}{{{I_2}}} = $

$\begin{array}{*{20}{l}} {{\rm{1}}\,{\rm{/}}\,{\rm{2}}} \end{array}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

{I_1} = \int \limits_0^\infty \,\,\frac{1}{{1 + {x^4}}}\,\,dx

and

{I_2} = \int \limits_0^\infty \,\,\frac{{{x^2}}}{{1\,\, + \,\,{x^4}}}\,\,dx

. Then

\frac{{{I_1}}}{{{I_2}}} =

View answer and explanation

Correct option: A

Option A (1) is correct because by substituting x = 1/t in I1, it transforms into I2, showing that I1 and I2 are equal.

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