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
