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Math 220-2: Kursobjekt

Appendix C Procedures

1.1 Antiderivatives

Procedure 1.1.5 Computing antiderivatives by inspection

1.2 Estimating area

Procedure 1.2.2 Estimating area
Procedure 1.2.5 Estimating net change

1.4 Definite integral

Procedure 1.4.2 Limit computation of integral

1.5 Fundamental theorem of calculus

Procedure 1.5.2 Computing integrals with antiderivatives

1.7 Substitution

Procedure 1.7.3 Substitution
Procedure 1.7.6 Definite integral substitution: 2-step

1.8 More substitution; area between curves

Procedure 1.8.1 Definite integral substitution: streamlined
Procedure 1.8.7 Area of region between intertwined curves

1.9 Volume via cross sections

Procedure 1.9.2 Volume via cross sections
Procedure 1.9.6 Volume of solid of revolution

1.10 Inverse functions

Procedure 1.10.9 Computing \((f^{-1})'(b)\)

1.13 Separable differential equations

Procedure 1.13.5 Separation of variables (algebraic form)

1.15 More on indeterminate forms

Procedure 1.15.2 Indeterminate forms

1.16 Inverse trigonometric functions

Procedure 1.16.5 General solution to trig equations

1.18 Integration by parts

Procedure 1.18.2 The art of by parts
Procedure 1.18.4 Integration workflow

1.19 Trigonometric integrals

Procedure 1.19.2 Integrating \(\sin^m x\cos^n x\)
Procedure 1.19.3 Integrating \(\tan^m x\sec^n x\)

1.20 Trigonometric substitution

Procedure 1.20.1 Inverse substitution: indefinite integral
Procedure 1.20.2 Trigonometric substitution
Procedure 1.20.3 Reference triangles
Procedure 1.20.7 Inverse substitution: definite integral

1.21 Rational functions

Procedure 1.21.4 Partial fraction decomposition

1.24 Improper integrals

Procedure 1.24.2 Improper integral: type I
Procedure 1.24.8 Improper integral: type II

1.25 Improper integrals: convergence tests

Procedure 1.25.5 Limit comparison test: type I
Procedure 1.25.6 Limit comparison test: type II

1.26 First-order linear differential equations

Procedure 1.26.3 Solving first-order linear equations

1.27 Modeling with differential equations

Procedure 1.27.1 Modeling with first-order differential equations