Question

求∫g(x)f(t)dt区间是从a到x的导数

Answer 1

∫[a→x] g(x)f(t) dt=g(x)∫[a→x] f(t) dt

因此(∫[a→x] g(x)f(t) dt)'

=( g(x)∫[a→x] f(t) dt )'

乘法求导公式

=g'(x)∫[a→x] f(t) dt+g(x)f(x)