Question-67963

Question Number 67963 by mhmd last updated on 02/Sep/19

Commented by mathmax by abdo last updated on 02/Sep/19

g e n e r a l l y i f F (x) = \int_{u (x)}^{v (x)} f (t) d t \Rightarrow F^{^{'}} (x) = v^{^{'}} (x) f (v (x)) - u^{^{'}} (x) f (u (x))

w e h a v e F (x) = \int_{0}^{x} t s i n (t) d t \Rightarrow F^{^{'}} (x) = {(x)}^{^{'}} (x s i n x) - {(0)}^{^{'}} (0 s i n 0)

= x s i n x .

Answered by mr W last updated on 02/Sep/19

i f G^{'} (x) = x \sin x, t h e n

F (x) = \int_{0}^{x} t \sin t d t = G (x) - G (0)

\Rightarrow F^{'} (x) = G^{'} (x) - 0 = x \sin x

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