Unformatted text preview: s it. Once the
parallelogram is created we can easily find the area of it using what we learned from chapter 10.
Area of Parallelogram = We know the tangent plane approximates the surface well near
. Two vectors that lie in the tangent plane are
and
. For our small parallelogram, our movement in the x and y direction is not one,
but a small change of
and
. So our vectors that represent the sides of the parallelogram are:
and
Thus the Area of Parallelogram can be derived below: Thus And finally the Surface Area = Example:
Find the surface area of the portion of the paraboloid lying above the xyplane. We need to know the projection of the surface in the xyplane: Let z = 0 to get the projection:
We need our partials to plug into the formula: ( Notice the change of coordinates to polar to make the limits a lot easier to find ) Summary of Section 13.4
1 Setting up and Evaluating a double integral that represents the Surface Area of a given surface Section 13.5 Triple Integrals
For now we will start with an integrand...
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 Spring '08
 Loukianoff,V
 Calculus, Integrals, Jacobian, coordinates

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