University of the Fraser Valley (UFV)

Defines Riemann sums, summations, and definite integrals with examples and diagrams

Highlights the properties of definite integrals and provides well-explained examples and diagrams

Explains the fundamental theorem of calculus and provides well-explained examples and physical interpretations of theorems

Describes the steps needed to use the substitution method of integration as well as examples.

Provides a concise description of how to solve the area between curves using integration. Includes examples and step-by-step instructions.

Explains how to set up an integral to solve for volume for general shapes and circular symmetry. Provides formulas and examples for solids of revolution; disk method, washer method, and shell method.

It contains step-by-step instructions on solving examples for integration by parts

Highlights common trigonometric substitutions and when and how to use them with examples

Details how to integrate some rational functions using partial decomposition. Includes broken down and step by step instructions to solve examples for linear factor cases and irreducible quadratic factor in the denominator.

Numeric approximation for an integral by using the midpoint rule, trapezoidal rule, and simpson's rule. Includes examples with diagrams and explanations.

Defines an improper integral and breaks down the steps for solving improper integrals with either an infinite domain of integration or with an unbounded integrated.

Defines the average value of a function and gives detailed examples on how to solve

Defines differential equations, gives step by step examples on how to soble separable differential equations (both general and particular solutions) and initial conditions,

Includes Definitions, notations, and examples. Explains convergence to a limit, monotone sequence theorem, and bounding terms.

An introduction to series, including definitions, relation to integration, theorems and detailed examples

Highlights theorems and gives detailed and explained examples on the divergence test

Highlights theorems and gives detailed and explained examples on the integral test for convergence

Highlights theorems and gives detailed and explained examples on the comparison test

Highlights theorems and gives detailed and explained examples on the alternating series test

Highlights theorems and gives detailed and explained examples on the ratio test