This course contains problem sets that accompany each section and module. In these problem sets, students are given an opportunity to apply the quantitative-reasoning skills they learned throughout the module.

Answers are only available to the problems with “Show Solution” links below the question prompt.

Module 1: Integration

• Problem Set: Approximating Areas
• Problem Set: The Definite Integral
• Problem Set: The Fundamental Theorem of Calculus
• Problem Set: Integration Formulas and the Net Change Theorem
• Problem Set: Substitution
• Problem Set: Integrals Involving Exponential and Logarithmic Functions
• Problem Set: Integrals Resulting in Inverse Trigonometric
• Module 1 Review Problems

Module 2: Applications of Integration

• Problem Set: Areas Between Curves
• Problem Set: Determining Volumes by Slicing
• Problem Set: Volumes of Revolution: Cylindrical Shells
• Problem Set: Arc Length of a Curve and Surface Area
• Problem Set: Physical Applications
• Problem Set: Moments and Centers of Mass
• Problem Set: Integrals, Exponential Functions, and Logarithms
• Problem Set: Exponential Growth and Decay
• Problem Set: Calculus of the Hyperbolic Functions
• Module 2 Review Problems

Module 3: Techniques of Integration

• Problem Set: Integration by Parts
• Problem Set: Trigonometric Integrals
• Problem Set: Trigonometric Substitution
• Problem Set: Partial Fractions
• Problem Set: Other Strategies for Integration
• Problem Set: Numerical Integration
• Problem Set: Improper Integrals
• Module 3 Review Problems

Module 4: Differential Equations

• Problem Set: Basics of Differential Equations
• Problem Set: Direction Fields and Numerical Methods
• Problem Set: Separable Equations
• Problem Set: The Logistic Equation
• Problem Set: First-order Linear Equations
• Module 4 Review Problems

Module 5: Sequences and Series

• Problem Set: Sequences
• Problem Set: Infinite Series
• Problem Set: The Divergence and Integral Tests
• Problem Set: Comparison Tests
• Problem Set: Alternating Series
• Problem Set: Ratio and Root Tests
• Module 5 Review Problems

Module 6: Power Series

• Problem Set: Power Series and Functions
• Problem Set: Properties of Power Series
• Problem Set: Taylor and Maclaurin Series
• Problem Set: Working with Taylor Series
• Module 6 Review Problems

Module 7: Parametric Equations and Polar Coordinates

• Problem Set: Parametric Equations
• Problem Set: Calculus of Parametric Curves
• Problem Set: Polar Coordinates
• Problem Set: Area and Arc Length in Polar Coordinates
• Problem Set: Conic Sections
• Module 7 Review Problems