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
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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