Area and Volume as a Double Integral

    Even though we can find the area between curves with single integral, it is often easier to compute area using a double integral. If over a region in the -plane then



gives the volume of the solid bounded above by the surface and bounded below by the region In the special case where we have  



To summarize, we have the following proposition.

Proposition (Area and Volume as a Double Integral) If is continuous and over a region in the -plane then



gives the volume of the solid bounded above by the surface and bounded below by the region In the special case where we have the area of the region

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Cite this as:
Area And Volume As A Double Integral
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
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