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Unformatted text preview: 1 5.1 Estimating with Finite Sums There is no easy formula for finding the area of a region bounded by a curve. Our goal for today is to develop a method for approximating the area by covering the region with a collection of rectangles. Consider a region bounded by a graph of a function f ( x ) a b x y f H x L We can estimate the area under the graph by adding the areas of the approx- imating rectangles. However, we must decide how tall our rectangles must be. Area ≈ Where Δ x = , and n is a number of subintervals. The long summation can be written in short form using sigma notation: Area ≈ The sums of this form are called 2 The approximation is determined by how you choose the height of each rect- angle. Definition S L : Left-endpoint Riemann Sum Choose the height of each rectangle on the interval [ x i ,x i +1 ]to be a b x y f H x L Area ≈ S R : Right-endpoint Riemann Sum Choose the height of each rectangle on the interval [ x i ,x i +1 ]to be a b x y f H x L Area ≈ S M : Midpoint...
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This note was uploaded on 10/02/2011 for the course MATH 1206 taught by Professor Llhanks during the Fall '08 term at Virginia Tech.
- Fall '08