Improper integral and rectangle method

[lokofer]

Improper integral and "rectangle" method

If we have a definite integral then..using "rectangle" method we can get the approximation:

\int_{a}^{b}f(x)dx \sim \sum_{n=0}^{N}f(a+nh)h

My question is..how do you define this method when b-->oo (Imporper integral?)...

 

[AKG]

The upper limit N must be such that a + Nh = b. If b -> oo, then make the upper limit N = oo.