After completing this section, students should be able to do the following.

  • Use integral notation for both antiderivatives and definite integrals.
  • Compute definite integrals using geometry.
  • Compute definite integrals using the properties of integrals.
  • Justify the properties of definite integrals using algebra or geometry.
  • Understand how Riemann sums are used to find exact area.
  • Define net area.
  • Approximate net area.
  • Split the area under a curve into several pieces to aid with calculations.
  • Use symmetry to calculate definite integrals.
  • Explain geometrically why symmetry of a function simplifies calculation of some definite integrals.