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Let $f$ be a continuous function satisfying $\int_{- π}^{t^{2}} (f (x) + x^{2}) d x = π + \frac{4}{3} t^{3}$ for all t, then $f (π^{2} / 4)$ is equal to

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π−π48

π2−π44

π2−π42

π−π416

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detailed solution

Correct option is D

Differentiating both sides, we haveft2+t42t=4t2ft2+t4=2t⇒ ft2=2t−t4so fπ24=fπ22=2π2−π24=π−π416.

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Let f be a continuous function satisfying ∫−πt2 f(x)+x2dx=π+43t3 for all t, then fπ2/4 is equal to

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Let $f$ be a continuous function satisfying $\int_{- π}^{t^{2}} (f (x) + x^{2}) d x = π + \frac{4}{3} t^{3}$ for all t, then $f (π^{2} / 4)$ is equal to