I'm working on a homework problem where I need to do something that looks like this (this isn't the exact question - I just want to check my reasoning for my approach). Given:
I need to find $df/dt$.
The approach I've come up with is:
In other words, to calculate $df/dt$, I can calculate $dg/dt$, and then integrate that with respect to $x$ from $a$ to $b$.
Is this correct? It feels right to me, but I'm not sure about bringing the limit inside the integral.
Apologies if the notation is bad. I wasn't sure how to: (a) make bigger integrals; (b) do multiple lines with the equal signs lining up; or (c) get the limit arrow part under the limit.