Module 8: Techniques of Integration
Not every integral yields to basic antiderivative rules. This module builds your integration toolkit: u-substitution, trigonometric integrals, integration by parts, and numerical approximation methods.
Your Progress
Learning Objectives
By the end of this module, you will be able to:
- Apply u-substitution to evaluate a wide range of integrals
- Evaluate integrals involving powers of trigonometric functions
- Use integration by parts, including the tabular method
- Approximate definite integrals numerically using the Trapezoidal Rule and Simpson's Rule
Module Lessons
u-Substitution
The most important single integration technique. Learn to choose u, change the variable, and handle definite integrals by changing bounds.
45-55 minutes
Integrals Involving Trig Functions
Evaluate integrals of powers of sine and cosine, use trig identities, and get an introduction to trig substitution.
40-50 minutes
Integration by Parts
Derive and apply the IBP formula, learn the LIATE rule, master the tabular method, and handle repeated IBP.
45-55 minutes
Numerical Integration
When antiderivatives cannot be found, approximate integrals using the Trapezoidal Rule and Simpson's Rule.
35-45 minutes