Explanation that Riemann integrals are not defined when the interval is unbounded but can often be found using limits. Mention of the alternative Lebesgue integral.

Using limits to evaluate improper integrals with unbounded limits of integration. Includes examples of integrating 1/(x^p) from 1 to infinity and integrating cos(x) from 0 to infinity.

Using limits to evaluate improper integrals involving functions that are unbounded over the specified limits of integration. Includes example of integrating 1/(x^p) between 0 and 1.

Definition of monotone bounded limits, the squeezing lemma for limits and improper integrals, and the comparison test for convergence of improper integrals.

The Comparison Test for determining convergence or divergence of improper integrals, with discussion and examples.

Determining whether an improper integral converges or diverges.

Solution (PDF) Page 2

Two questions which involve determining whether an improper integral will converge or diverge.

Solution (PDF)

An integral with an infinite upper limit of integration to be evaluated.

Solution (PDF)^# Page 1

Determining whether twenty-two different improper integrals are convergent or divergent, and evaluating the limits of six integrals using the Fundamental Theorem.

Solution (PDF - 4.0 MB) Pages 91 to 93