JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

Let

f

be a continuous function satisfying

\int\limits_{{-\pi}}^{t^2}\left(f(x)+x^2\right) \mathrm{d} x=\pi+\frac{4}{3} t^3

for all

t

, then

f\left(\pi^2 / 4\right)

is equal to

View answer and explanation

Correct option: D

\pi-\frac{\pi^4}{16}

Option D (

\pi-\frac{\pi^4}{16}

) is correct because differentiating the given equation and substituting

t = \frac{\pi}{2}

yields the value of

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

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