Approximating the area under a curve

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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 $n\to \infty$ .