If f(x) = _0^x t t ,dt ,, then f'(x) = - Vidyadip

MCQ

If $f(x) = \int_0^x {t\sin t\,dt\,,} $ then $f'(x) = $

A
$\cos x + x\sin x$
✓
$x\sin x$
C
$x\cos x$
D
None of these

✓

Answer

Correct option: B.

$x\sin x$

b
(b) Since,$f(x) = \int_0^x {t\sin tdt} $.

Now, according to Leibnitz's rule,

$f'(x) = x\,\sin x.(1) - 0 = x\sin x$.

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