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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 xyplane. 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 xyplane 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.
 Spring '08
 Loukianoff,V
 Calculus, Integrals

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