For any integer $n$, the integral $\mathop \smallint \nolimits_0^\pi \,\,{e^{{{\cos }^2}x}}\,\,{\cos ^3}\left( {2n + 1} \right)\,\,x\,\,\;dx\;$ has the value

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

For any integer

n

, the integral

\int \nolimits_0^\pi \,\,{e^{{{\cos }^2}x}}\,\,{\cos ^3}\left( {2n + 1} \right)\,\,x\,\,\;dx\;

has the value

View answer and explanation

Correct option: C

\mathrm{0}

Option C (0) is correct because the integrand is an odd function with respect to x = π/2, making the integral over the interval [0, π] equal to zero.

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