If I have a limit going to infinity with Σ with n on top and i=1 on bottom that has (4/n) √(8+(4i/n)) inside and I know that A=0 and B=4 for the upper and lower limit when changing this into an integral. So what is f(x)? Why wouldn't it just be √x?

Answer 1

∑(4/n)√(8+(4k)/n)
This is supposed to be ∑ f(x_i) ∆x
so you want
∫[0..4] √(8+x) dx

Answer 2

But what would represent f(x) in that circumstance? Like what is the function that has xi plugged into it?

Answer 3

huh? I showed you the integral, which is f(x) dx
If you go to some math web site, you will find that the sum and the integral are the same value.

xi = i (4/n)

I just used k, since most math sites interpret i as the imaginary number root(-1)