JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

The value of the constant

a>0

such that

\int_0^a\left[\tan ^{-1} \sqrt{x}\right] d x=\int_0^a\left[\cot ^{-1} \sqrt{x}\right] d x

, where

[\cdot]

denotes the greatest integer function, is

View answer and explanation

Correct option: A

\frac{2(3+\cos 4)}{1-\cos 4}

Option A (

\frac{2(3+\cos 4)}{1-\cos 4}

) is correct because it is derived by solving the equation after simplifying the integrals using the greatest integer function.

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