Integration, Areas & Improper Integrals

Connect accumulated area with antiderivatives and limits. Practice definite integration, the fundamental theorem, substitution, integration by parts and improper integrals, including elementary probability-area normalization. Prerequisite: limits and derivatives. Analytical questions address signed versus geometric area, singularities, tail convergence and why a curve approaching zero need not have finite area.

Further reading:

• Paul Dawkins: Definite integrals
• Paul Dawkins: Integration by parts
• Paul Dawkins: Improper integrals

Cover: Photo by Barnabas Davoti on Pexels.