JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

I_n=\int\limits_{0}^1\left(\cos ^{-1} x\right)^n \mathrm{~d} x

then

I_6-360 I_2

is given by

View answer and explanation

Correct option: B

6\left(\frac{\pi}{2}\right)^5-120\left(\frac{\pi}{2}\right)^3

Option B (

6(\frac{\pi}{2})^5-120(\frac{\pi}{2})^3

) is correct because after applying integration by parts twice, the expression

I_6 - 360I_2

simplifies to

6(\frac{\pi}{2})^5-120(\frac{\pi}{2})^3

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