In this section, we will define what it means for an integral to be improper and begin investigating how to determine convergence or divergence of such integrals.

We might have one (or both) of the limits of integration being infinite.

The function could have an infinite discontinuity somewhere in the interval [a, b].

We will use limits. If exists, then we say I converges to this value, otherwise it diverges.

Suppose f has an infinite discontinuity at x = a. If exists, then we say I converges to this value, otherwise it diverges. Suppose f has an infinite discontinuity at x = b. If exists, then we say I converges to this value, otherwise it diverges.

Determine whether the integral converges or diverges. If it converges, state to what value.