Ch13Notes

# Find where the two curves intersect figure out where

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Unformatted text preview: out where the ray should start and where it should end. Area = Summary of Section 13.3 1 Setting up and Evaluating double integrals in Polar Coordinates 2 Finding the Area of a region bounded by Polar Equations Section 13.4 Surface Area We can use a double integral to find the Surface Area of some surface. We will also use this idea later on in Chapter 14 to set up a new type of integral called a Surface Integral. Understanding the following derivation is important for that reason. We will derive the formula for Surface Area: Let S represent our surface and Q represent its projection on the xy-plane. We will partition the region Q up into rectangular subregions as we have done before. Let be a corner point in one of the subregions. Let and represent the length and width of our subregion. Then represents the Area of our rectangular region. The area in the xy-plane is a projection of part of the surface S. Let’s call this small patch . We want to approximate the surface area of that small patch . We will create a Parallelogram that approximate...
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## This note was uploaded on 03/05/2014 for the course MATH 101c taught by Professor Loukianoff,v during the Spring '08 term at Ohlone.

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