
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.