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