The value of $\mathop \smallint \limits_0^{2\pi } {\cos ^{99}}\,\,x\,dx$, is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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The value of

\int \limits_0^{2\pi } {\cos ^{99}}\,\,x\,dx

, is

View answer and explanation

Correct option: D

\mathrm{0}

Option D (0) is correct because the integral of cos⁹⁹(x) from 0 to 2pi evaluates to zero due to the properties of even and odd functions over symmetric intervals.

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