Integral Calculus
Besides the examples on this page, please see the discussion in ["BasicCalculus"].
Definite and Indefinite Integrals
The Definite Integral
- o The definition of area under curve o Relation between velocity and area o Definition of Integral o The Fundamental Theorem of Calculus
Indefinite Integrals and Change
- o Indefinite Integrals o Physical Intuition
Substitution and Symmetry
- o The Substitution Rule o The Substitution Rule for Definite Integrals o Symmetry
Applications to Areas, Volume, and Averages
Using Integration to Determine Areas Between Curves
Computing Volumes of Surfaces of Revolution
Average Values
Polar coordinates and complex numbers
- o Polar Coordinates o Areas in Polar Coordinates o Complex Numbers o Polar Form o Complex Exponentials and Trig Identities o Trigonometry and Complex Exponentials
Integration Techniques
Integration by parts
Trigonometric integrals
- o Some Remarks on Using Complex-Valued Functions
Trigonometric substitutions
Factoring polynomials
Integration of Rational Functions Using Partial Fractions
Approximating Integrals
Improper Integrals
- o Convergence, Divergence, and Comparison