Mathematics

If $$f(x)=\displaystyle\int_{0}^{x}t\sin tdt$$, then $$f'(x)$$ is


ANSWER

$$x\sin x$$


SOLUTION
$$f(x)=\displaystyle\int_{0}^{x}t.\sin t.dt$$

$$Using \space Leibniz \space Rule \space $$

$$f'(x)=\left (tsint\right)_0^x =xsinx$$

$$\therefore$$ Answer is $$(B)$$
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Single Correct Medium Published on 17th 09, 2020
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