About Course

Step into the world of integration by exploring how to “reverse” differentiation. In this focused mini-course, you’ll learn to recognize the patterns that produce familiar functions, apply the right rules to reconstruct antiderivatives, and wield substitution to tackle more complex expressions. You’ll also appreciate why every solution must include an arbitrary constant—understanding how that constant captures families of curves and encodes initial conditions. Through clear, real-world analogies and hands-on practice, you’ll build the toolkit you need for success on the AP Calculus AB exam and for any application that requires finding areas, solving differential equations, or modeling accumulation.

What Will You Learn?

  • Identify and apply the fundamental reversal rules for basic functions
  • Combine rule-based antiderivatives for sums, constants, and power functions
  • Simplify and integrate complex expressions using the substitution technique
  • Appreciate the essential role of the constant of integration in defining solution families
  • Use initial conditions to determine unique antiderivatives in real-world problems

Course Content

1. Basic Antiderivative Rules
Learn to spot and apply the fundamental reversal patterns for simple functions. You’ll see how sums, constants, and power-law behaviors translate directly into antiderivatives, and you’ll practice rebuilding common families of functions from their rates of change.

  • 1.1 Recognizing Core Antiderivative Patterns
  • 1.2 Applying Sum, Difference & Constant-Multiple Rules
  • 1.3 Reconstructing Polynomials & Exponential Families

2. The Substitution Technique
Discover how to simplify complex expressions by temporarily introducing a new variable. You’ll master the art of choosing effective substitutions, transform tangled expressions into basic patterns, and learn to reverse the change once you’ve found the antiderivative.

3. The Constant of Integration
Understand why every antiderivative carries an arbitrary constant and how that constant represents a family of solutions. You’ll learn to use initial or boundary conditions to pin down a unique solution—and see why neglecting the constant can lead to missed answers in applications.