How do limits help resolve improper integrals?

Question

anonymous · Answer

well  an improper integral is the derivative of a  f(x) but not all functions are differentiable as we see with the FTC . So how do we define if a function actually exists? well we do so by  making an integral where the first part is bounded by the first point and everything under it if that b=part is convergent well...that doesn't solve much does it? so lets check the other side which is b does that go to a number? if both sides go to a number it converges and it exists but if one part is divergent we can assume the function doesn't differentiate well around this point . We then take a limit as a or b approaches some number , we can say infinity due to discreteness and voila we can determine the limits of both sides of the curve are convergent or not and done.

anonymous · Answer

if im wrong or someone can greatly simplify this id be soo happy

2yoututu11 · Answer

From the looks of it,it looks legit