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Unformatted text preview: out where the ray should start and where it should end.
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
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
represent the length and width of our subregion. Then
represents the Area of our rectangular
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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