Calculus For Dummies, 2nd Edition

Part V

Integration and Infinite Series

Check out my online article, “Integration by Parts and Going in Circles” at www.dummies.com/extras/calculus.

In this part …

• The meaning of integration: Integration is basically just fancy calculus addition. It works by sort of slicing up something into tiny bits (actually infinitesimal bits) and then adding up the bits to get the total. This allows you to find the total of things — say, the total volume of some weird bell-shaped object — that can’t be handled by simple, pre-calculus formulas.
• The fundamental theorem of calculus: Integration is basically differentiation in reverse — namely, antidifferentiation. There’s an intimate yin/yang connection between integration and differentiation which this part looks at from several angles.
• Techniques for calculating antiderivatives: Substitution, integration by parts, trig integrals, and partial fractions.
• Integration word problems: Calculating the area between curves, finding volume with the washer method, computing arc length and surface area, and improper integrals.
• L’Hôpital’s rule: A nice trick for solving limit problems.
• Taming infinity: Ten tests for the convergence or divergence of infinite series.