let-considere-f-and-u-differenciable-function-prove-that-d-dt-a-u-t-f-t-x-dx-a-u-t-f-t-t-x-dx-f-t-u-t-u-t-

Question Number 33122 by abdo imad last updated on 10/Apr/18

l e t c o n s i d e r e f a n d u d i f f e r e n c i a b l e f u n c t i o n p r o v e

t h a t \frac{d}{d t} (\int_{a}^{u (t)} f (t, x) d x) = \int_{a}^{u (t)} \frac{\partial f}{\partial t} (t, x) d x + f (t, u (t)) u^{^{'}} (t)