Master Integrals

Learn everything from Integrals, then test your knowledge with 400+ practice questions

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“Krista does an excellent job of explaining the smallest details in every example. She never assumes you understood where a number came from. I’ve learned much more from her than I have my own lecture videos at ASU!”

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Course Summary

Learn everything you need to know to get through Integrals and prepare you to go into Applications with a solid understanding of what’s going on. Video explanations, text notes, and quiz questions that won’t affect your class grade help you “get it” in a way most textbooks never explain.

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Course outline

The curriculum includes:

Antiderivatives and indefinite integrals
- Indefinite integrals
- Properties of integrals
- Find f given f''
- Find f given f'''
- Initial value problems
Definite integrals
- Definite integrals
- Area under or enclosed by the graph
- Definite integrals of even functions and odd functions
Riemann sums
- Summation notation, finding the sum, expanding, collapsing
- Riemann sums with left endpoints, right endpoints, and midpoints
- Overestimation and underestimation
- Limit process to find area on [a,b] and [-a,a]
- Trapezoidal rule
- Simpson's rule
Error bounds
- Midpoint rule error bound
- Trapezoidal rule error bound
- Simpson's rule error bound
Fundamental theorem of calculus (FTC)
- Part 1 of the FTC
- Part 2 of the FTC
- Net change theorem
U-substitution
- U-substitution
- U-substitution in definite integrals
Integration by parts
- Integration by parts
- Integration by parts two times and three times
- Integration by parts with u-substitution
- Prove the reduction formula
- Tabular integration

Partial fractions
- Distinct linear factors
- Distinct quadratic factors
- Repeated linear factors
- Repeated quadratic factors
- Rationalizing substitutions
- How to factor a difficult denominator
- Two ways to find the constants
Trigonometric integrals
- Trigonometric integrals
- sin^m cos^n, odd m
- sin^m cos^n, odd n
- sin^m cos^n, m and n even
- tan^m sec^n, odd m
- tan^m sec^n, even n
- sin(mx) cos(nx)
- sin(mx) cos(nx)
- cos(mx) cos(nx)
Hyperbolic integrals
- Hyperbolic integrals
- Inverse hyperbolic integrals
Trigonometric substitution
- Setting up for trig substitution problems
- Secant substitutions
- Sine substitutions
- Tangent substitutions
- Quadratic functions
Improper integrals
- Improper integrals
- Case 1 [a,infinity)
- Case 2 (-infinity,b]
- Case 3 (-infinity,infinity)
- Case 4 (discontinuity at b)
- Case 5 (discontinuity at a)
- Case 6 (discontinuity between a and b)
- Comparison theorem
Reduction formulas