MATH 111 Lecture Notes - Lecture 21: Riemann Sum, Fax
13 Jul 2015
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Document Summary
Finding the area of regions with straight lines is easy. With a region with curved lines, the area can be estimated in many ways: Divide the region into multiple sections, and estimate the area by creating a rectangle within each region and finding the area of each section. There are two ways to create rectangles with this method: using the left endpoint of each section, and using the right endpoint of each section. As n (the number of sections that the region is divided into) increases, the accuracy of the area estimation increases. A= limn rn = limn [ f(x1) x + f(x2) x + + f(xn) x ] This function is the same even when using left endpoints. A= limn [ f(x1*) x + f(x2*) x + + f(xn*) x ] Taking the height of the ith rectangle to be the value of f at any number xi* in the ith subinterval [xi-1, xi]
