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


In class