Module 6: Integration
Welcome to the second major branch of calculus! This module introduces antiderivatives, Riemann sums, the definite integral, and the Fundamental Theorem of Calculus that connects differentiation and integration.
Your Progress
Lessons 1-4
Practice
Module Quiz
Review
Learning Objectives
By the end of this module, you will be able to:
- Compute antiderivatives using basic rules
- Approximate areas under curves using Riemann sums
- Evaluate definite integrals using the Fundamental Theorem of Calculus
- Apply FTC Part 2 and the Net Change Theorem
Module Lessons
1
Antiderivatives and Indefinite Integrals
Reverse the process of differentiation. Learn the basic integration rules and the role of the constant of integration.
35-45 minutes
2
Riemann Sums and Area
Approximate the area under a curve using rectangles. Understand left, right, and midpoint sums.
40-50 minutes
3
Definite Integral and FTC Part 1
Define the definite integral as a limit of Riemann sums and discover FTC Part 1.
35-45 minutes
4
FTC Part 2 and Net Change
Evaluate definite integrals efficiently and apply the Net Change Theorem.
35-45 minutes