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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 |
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