If $I_{10}=\int_0^{\pi / 2} x^{10} \sin x d x$, then $I_{10}+90 I_8$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

I_{10}=\int_0^{\pi / 2} x^{10} \sin x d x

, then

I_{10}+90 I_8

View answer and explanation

Correct option: B

10(\pi / 2)^9

Option C is correct because the reduction formula for the integral of x^n sin(x) involves integration by parts, leading to the given relationship between I_10 and I_8.

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