Question

evaluate the following:

Answer 1

1. \[\frac{ d }{ dx }[\int\limits_{1}^{x}t ^{3}dt] = ?\]
2. \[\frac{ d }{ dx }[\int\limits_{3}^{sinx}\frac{ 1 }{ 1+t ^{2} }dt] = ?\]

Answer 2

@zepdrix

Answer 3

For the first one, we can apply the FTC Part 1.\[\large \color{cornflowerblue}{\frac{d}{dx}\int\limits_a^x f(t)dt=f(x)}\]

Answer 4

\[\huge \frac{d}{dx}\int\limits_1^x t^3 dt=x^3\]Understand how we applied that? :D
We can go into a little bit further detail if it's confusing.

Answer 5

Ok ok lemme explain it a tiny bit further, because it will help us on the next problem anyway.

Answer 6

hm.. can we go into further detail please? haha i always need to see the process in oro understand something :p

Answer 7

thanks!