Chapter 4
Approximating Area with Riemann Sums
IN THIS CHAPTER
Calculating Riemann sums using left and right rectangles
Using midpoint rectangles to improve Riemann sum approximation
Approximating area using trapezoids
Understanding and applying Simpson’s rule for finding Riemann sums
In Chapter 1, I show you how to use a definite integral to state an area problem on the xy-graph in mathematically precise terms. You find that, in some cases, you can calculate the exact value of a definite integral simply by applying a bit of geometry.
In this chapter, I show you how to approximate the value of a definite integral by slicing an area into a finite number of rectangles, and how to calculate the resulting Riemann sum.
If you’ve already taken a college-level Calculus 1 course, this material may be review; otherwise, you may be discovering it for the first time. Either way, here you review the three methods for finding a Riemann sum that I covered briefly in Chapter 1. Next, I show you two more methods — the Trapezoid rule and Simpson’s rule — which both provide successively better estimates. ...
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