Continuing from this forum here, suppose that $f(x)=\dfrac{e^{8x}}{8}$ and $f'(x) = e^{8x}$. I was told that : $\displaystyle\lim_{\Delta x \to 0}\sum_{x=0}^{2} [(f'(x)e^{6x}\Delta x] = \int_{0}^{2} e^{14x}dx $
How can this be proven ?
Note: I don't quite understand whether some are supposed to be $dx$ or $\Delta x$. I'm not able to confirm it right now but I think it is supposed to be which ever make sense and can get you to prove that it is equal to $\int_{0}^{2} e^{14x}dx $. I do need recommendation regarding this. I will edit the question accordingly if it is proven be to one or the other.