Mathematics

If $$f(x)=\displaystyle \int_{0}^{x}{t(\sin x-\sin t)dt}$$ then $$f'(x)$$?


SOLUTION
Given,
$$f(x)= \int_{0}^{x} t (\sin x- \sin t) dt;$$
Now applying Libnitz's rule fon differentiating under integration we get,
$$f'(x)= x (\sin x- \sin x ).1-0+ \int_{0}^{x} t \cos x dt$$
on, $$f'(x)= (\cos x)(x^{2}/2)$$
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Subjective Medium Published on 17th 09, 2020
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