How do you use the second fundamental theorem of Calculus to find the derivative of given #int arctan(3t) dt# from #[4,1/x]#?
FTC part 2 says that
here you want
we can start by separating out the integration limits so they match the theorem
the red term is constant and can be ignored. in fact we could have specified that a = 4 and continued with the basic formulation of FTC pt 2
the green term is not exactly in the form required but the FTC pt 2 can be expressed in terms of a new variable u as
So we can say that