|Module 15 - Riemann Sums and the Definite Integral|
|Introduction | Lesson 1 | Lesson 2 | Lesson 3 | Self-Test|
In this module you will learn how to estimate areas by filling the region with rectangles and adding their areas. Such sums are called Riemann sums, and you will use them to estimate the area of a region and also to find its exact area. The investigation of Riemann sums will lead to the definite integral, a basic construct of calculus.
You know how to find the areas of regular geometric objects such as rectangles and triangles, but how would you find the area of a region when some of the boundaries are curves? Consider the area of the shaded region below. How would you find its area?
15.1 - Right-hand Riemann Sums
15.2 - Left-hand Riemann Sums and the area Program
15.3 - The Definite Integral
After completing this module, you should be able to do the following:
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