Calc 2, Lec 13B, Proof Using Comparison Test for Improper Integrals, Volumes of Solids of Revolution

Calculus 2, Lecture 13B.

(0:00) Prove that the improper integral of (2 + sin(t))/(t^2 + 1) from 1 to infinity converges using the comparison test.
(8:14) Volumes of solids of revolution. Example: Rotate the region bounded by y = x^2 between x = 0 and x = 2 about the x-axis.
(18:04) Rotate the region bounded by y = x^2 and y = sqrt(x) between x = 0 and x = 2 about the horizontal line y = -2.
(27:51) Check answer with Mathematica.