If $f(0)=f^{\prime}(0)=0$ and $f^{\prime \prime}(x)=\tan ^2 x$ then $f(x)$ is

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

f(0)=f^{\prime}(0)=0

and

f^{\prime \prime}(x)=\tan ^2 x

then

f(x)

View answer and explanation

Correct option: A

\log \sec x-\frac{1}{2} x^2

Option A (

\log \sec x-\frac{1}{2} x^2

) is correct because integrating

f''(x) = \tan^2 x

twice and applying the initial conditions

f(0) = f'(0) = 0

yields this result.

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