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integrate the inside integral you would get the single integral: This should look familiar. This is how you found area in 101A.
Example:
Write the area of the unit circle with a definite integral. Now write the area of the unit circle with a double integral. Notice if you integrate the inside integral you end up with the same definite integral right above it. Once you add an integrand f(x,y) , then our double integral represents volume under the surface f(x,y).
For example: This double integral represents the volume of a solid. Sketch the solid.
represents the surface above the region R (in the xyplane) given by the limits
We just learned the skill of representing the region R from the limits. Is there a way to write the length of the rectangular box, f(x,y) as an integral?
So I can take my double integral above and rewrite it as a triple integral. We will look in depth at triple integrals in section 13.5
Summary of Section 13.1
1 Setting up a double integral 2 Evaluating a double integral 3 Sketching the region represented by a double integral 4 Changing the order of integration for a double integral 5 Sketching the solid represented by a double integral Section 13.2 Area, Volume and Center of Ma...
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 Spring '08
 Loukianoff,V
 Calculus, Integrals, Jacobian, coordinates

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