JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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\int_{-4}^4 \frac{\sin ^{-1}(\sin x)+\cos ^{-1}(\cos x)}{\left(1+x^2\right)\left(1+\left[\frac{x^2}{17}\right]\right)} d x=\log \left(\frac{\left(1+x^2\right)}{a}\right)

+b \pi \tan ^{-1}\left(\frac{c-\pi}{1+c \pi}\right)

(where, [] denotes greatest integer function), then number of ways in which

a-(2 b+c)

distinct object can distributed amono

a-5

equally, is

View answer and explanation

Correct option: A

\frac{9 !}{(3 !)^3}

Option A (

\frac{9 !}{(3 !)^3}

) is correct because after evaluating the integral and comparing with the given expression, the number of ways to distribute the objects is

\frac{9 !}{(3 !)^3}

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