**Learning Objectives**

- Recognize the type of problem where definite integrals are useful
- Think of definite integrals as fancy sums
- Interpret definite integrals of rates and of densities
- Use the Fundamental Theorem of Calculus to evaluate integrals algebraically
- guess and check, substitution, integration by parts

- Use Mathematica to evaluate integrals
- Solve applied problems with integration
- Work with probability distributions described by density functions (pdfs) and cumulative distribution functions (cdfs)
- Compute probabilities
- Find the mean and median of probability distributions

- Evaluate definite integrals numerically – left, right, trapezoid, midpoint, and Simpson

**Resources**

- Textbook: 5.1-5.3, 6.1-6.2, 7.1-7.2, 8.7-8.8.
- Notes on the Fundamental Theorem of Calculus : integration of rates
- Notes on the Second Fundamental Theorem : every function is a derivative of some function
- How close is the tangent line approximation?
- How accurate is numerical integration?

**In class**

- Work integral problems
- More problems
- Algebraic techniques of integration
- Integrating with Mathematica
- Probability notes
- Probability problems
- Numerical integration via function approximation notes
- Numerical integration problems

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