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Question Number 137378 by benjo_mathlover last updated on 02/Apr/21

G i v e n {\int_{0}}^{x} f (t) d t = x^{2} \sin (π x)

f i n d f (2) .

Answered by EDWIN88 last updated on 02/Apr/21

\frac{d}{dx} [\int_{0}^{x} f (t) dt] = \frac{d}{dx} [x^{2} \sin (π x)]

\Rightarrow f (x) = 2 x \sin (π x) + π x^{2} \cos (π x)

\Rightarrow f (2) = 4 \sin (2 π) + 4 π \cos (2 π) = 4 π

Answered by mathmax by abdo last updated on 02/Apr/21

\int_{0}^{x} f (t) dt = x^{2} \sin (π x) \Rightarrow f (x) = 2 xsin (π x) + π x^{2} \cos (π x) \Rightarrow

f (2) = 4 \sin (2 π) + 4 π \cos (2 π) = 4 π