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