JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

Let

f

be a continuous function satisfying

\int\limits_{0}^{t^2}\left(f(x)+x^2\right) d x=\frac{4}{3} t^3, \forall t>0

. Then

f\left(\frac{\pi^2}{4}\right)

is equal to

View answer and explanation

Correct option: C

\pi\left(1-\frac{\pi^3}{16}\right)

Option C (

\pi(1-\frac{\pi^3}{16})

) is correct because it is the value of the function

f(x)

evaluated at

x = \frac{\pi^2}{4}

after solving the given integral equation.

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