Let f be a continuous function satisfying ∫₀^(t)²(f(x)+x²) d x=4/3 t³, t > 0. Then f((π²)/4) is equal to:

Integral Calculus: JEE Main 2023 Mathematics question

JEE Main 2023 · 10 Apr, Evening shift · Q3319

JEE Main 202310 Apr, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

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 :

JEE Main 2023 · 10 Apr, Evening shift · Q3319

JEE Main 202310 Apr, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

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 :