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Definite Integration question

2023 · 10 Apr · Shift 2 · Q26

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PYQ Library
JEE Main
Mathematics
Definite Integration
2023 · 10 Apr · Shift 2 · Q26

Definite Integration question

2023 · 10 Apr · Shift 2 · Q26

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

Let

f

be a continuous function satisfying

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

. Then

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

is equal to :

A
$-\pi\left(1+\frac{\pi^{3}}{16}\right)$
B
$\pi\left(1-\frac{\pi^{3}}{16}\right)$
C
$-\pi^{2}\left(1+\frac{\pi^{2}}{16}\right)$
D
$\pi^{2}\left(1-\frac{\pi^{2}}{16}\right)$

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