$\mathop \smallint \limits_0^\pi \,k{\left( {\pi \;x\,\, - \,\,{x^2}} \right)^{100}}\sin \,\,2x\,\,\;dx$ is equal to

$\frac{1}{2}\,\,\left( {{\pi ^{100}} - \,\,{\pi ^{97}}} \right)$

$\frac{1}{2}\,\,\left( {{\pi ^{100}} + \,\,{\pi ^{97}}} \right)$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Analyzing +4 | -1

\int \limits_0^\pi \,k{\left( {\pi \;x\,\, - \,\,{x^2}} \right)^{100}}\sin \,\,2x\,\,\;dx

is equal to

View answer and explanation

Correct option: D

\mathrm{0}

Option D (0) is correct because the integral evaluates to zero due to the symmetry properties after applying the substitution x = pi - x.

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