The value of the integral $\mathop \smallint \nolimits_0^{\pi /2} \,\,({\sin ^{100}}\,\,x - \,\,{\cos ^{100}}\,\,x)\,\,dx$ is

$\frac{{100\,\,!}}{{{{\left( {100} \right)}^{100}}}}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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The value of the integral

\int \nolimits_0^{\pi /2} \,\,({\sin ^{100}}\,\,x - \,\,{\cos ^{100}}\,\,x)\,\,dx

View answer and explanation

Correct option: D

Option D (0) is correct because the integral of sin¹⁰⁰(x) from 0 to pi/2 is equal to the integral of cos¹⁰⁰(x) from 0 to pi/2, resulting in a difference of 0.

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