Applications of the definite integral

With the definite integral we compute areas enclosed between two curves and volumes of solids of revolution, using the two complementary methods of discs (revolution about the $x$ axis) and cylindrical shells (revolution about the $y$ axis). We then see how symmetries (even and odd functions) simplify the calculations and how the integral extends to unbounded domains (improper integrals).

• Area between two curves
• Volumes of revolution - the disc method
• Volumes of revolution - the cylindrical shell method
• Even and odd functions
• Improper integrals