JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

f^{\prime}(x)=\tan ^{-1}(\sec x+\tan x), x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)

and

f(0)=0

, then the value of

f(1)

View answer and explanation

Correct option: A

\frac{\pi+1}{4}

Option A is correct because the derivative simplifies to

f^{\prime}(x)=\frac{\pi}{4}+\frac{x}{2}

, and integrating with the given condition

f(0)=0

yields

f(1)=\frac{\pi+1}{4}

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