7.8 Improper Integrals. The comparison theorem, given for Type 1A and Type 2A improper integrals, but similar versions hold for all improper integrals. Several examples in depth, and strategies for finding simpler functions to compare to.
7.7 Approximate Integration. General framework for approximate integration, then specialized to left, right, and midpoint rules. Trapezoid rule as average of left- and right-endpoint rules. Examples with Mathematica, and discussion of nature of under- or over-estimate depending on rule chosen and whether the function is increasing, decreasing, concave up, or concave down.