# Integrals as Net Change

## The Big Picture

## Net Change and Antiderivatives

Images taken from the AP©

## Net Change and the Graph of f '

Images taken from the AP©

## Practice Problems

Beyond Calculus

**Pre-Calculus**

- Linear Equations
- Solving Polynomial Equations
- Functions and Domain
- Piecewise Functions
- Topics in Trigonometry
- Exponentials and Logarithms

**Limits and Continuity**

- The Three Tiers of Limits
- Properties of Limits
- Continuity
- Intermediate Value Theorem
- Limits to Infinity
- Analyzing Functions using Limits

**Derivatives**

- Definition of the Derivative
- Tanget Lines / Normal Lines
- Differentiability
- Power Rule
- Different Derivatives
- Product Rule
- Quotient Rule
- Chain Rule
- Implicit Differentiation
- Derivatives of Inverse Functions
- Derivatives and Physics

**Applications of Derivatives**

- Rates of Change
- Increasing / Decreasing
- Maxima and Minima
- First Derivative Analysis
- Concavity and Inflection Points
- First and Second Derivative Analysis
- Graphical Interpretations
- Mean Value Theorem
- Optimization
- Related Rates
- Linearization
- L'Hospital's Rule

**Integrals**

- Estimating the Integral Using
- Definition of the Integral
- Integration Using Geometry
- Anti-Derivatives
- Definite Integrals
- Average Value of a Function
- Fundamental Theorem of Calculus
- Integration by Substitution
- Slope Fields
- Initial Value Problems
- Differential Equations

**Applications of Integrals**

- Exponential Growth and Decay
- Net Change
- Integrals and Physics
- Areas Between Curves
- Volumes of Solids Given a Base and Cross Sections
- Solids by Revolution:

Beyond Calculus is designed for students currently taking Calculus.

Images taken from the AP©

Images taken from the AP©