$\mathop \smallint \nolimits_{ - \pi }^\pi \,\,\frac{{{{\sin }^4}\,\,x}}{{{{\sin }^4}\,\,x\,\, + \,\,{{\cos }^4}\,\,x}}\,\,dx$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

\int \nolimits_{ - \pi }^\pi \,\,\frac{{{{\sin }^4}\,\,x}}{{{{\sin }^4}\,\,x\,\, + \,\,{{\cos }^4}\,\,x}}\,\,dx

is equal to

View answer and explanation

Correct option: D

\pi

Option D (

\pi

) is correct because the integral simplifies to a constant value after applying trigonometric identities and properties of definite integrals.

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