I am having a problem with this exercise. Please help.
I need to calculate F'(x) such that $F(x)=\int_{x}^{x^2} g(t)dt$ such that g(x) is a continuous function
Thank you in advance
I am having a problem with this exercise. Please help.
I need to calculate F'(x) such that $F(x)=\int_{x}^{x^2} g(t)dt$ such that g(x) is a continuous function
Thank you in advance
You can use this formula
$ {d\over dx}\, \int_{f_1(x)}^{f_2(x)} g(t) \,dt = g[f_2(x)] {f_2'(x)} - g[f_1(x)] {f_1'(x)} \,,$
which is known as Leibniz rule.
Hint: if $G$ is any indefinite integral of $g$, we have that $\int_{x}^{x^2} g(t)dt=G(x^2)-G(x)$
Hint