An improper integral is said to converge if the limit of the integral exists. An improper integral is said to diverge when the limit of the integral fails to exist.

How do you know if improper integrals converge or diverge?

Convergence and Divergence. If the limit exists and is a finite number, we say the improper integral converges . If the limit is ±∞ or does not exist, we say the improper integral diverges .

How do you show that an improper integral converges?

∫ a b f ( x ) d x = lim t → a + ∫ t b f ( x ) d x . In each case, if the limit exists, then the improper integral is said to converge. If the limit does not exist, then the improper integral is said to diverge.