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

  • Express the sum of n terms using sigma notation.
  • Apply the properties of sums when working with sums in sigma notation.
  • Understand the relationship between area under a curve and sums of areas of rectangles.
  • Approximate area of the region under a curve.
  • Compute left, right, and midpoint Riemann sums with 10 or fewer rectangles.
  • Understand how Riemann sums with n rectangles are computed and how the exact value of the area is obtained by taking the limit as .