Question

how to know wether the integral converges or diverges?

Answer 1

(1) integrate the function.
(2) evaluate from a to b. Take a limit if a or b is a horizontal/vertical asymptote. if answer is finite then it converges, otherwise it's unbounded (infinity) and it diverges.

Here's one that diverges:
\[\int\limits_{0}^{\infty} e^{x} = \lim_{t \rightarrow \infty} e^{t} - e^{0} = \infty \]

Answer 2

oh. i get it.thank you so much.