## anonymous 5 years ago how to know wether the integral converges or diverges?

1. anonymous

(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: $\int\limits_{0}^{\infty} e^{x} = \lim_{t \rightarrow \infty} e^{t} - e^{0} = \infty$

2. anonymous

oh. i get it.thank you so much.