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Double Integral

  1. Nov 28, 2003 #1
    OK OK I know Double Integral is from Multivar Calculus,

    I was just wondering what we use it for... I heard is good for volumes, but can't yhou also find volumes by just 1 integral?

    And also, aside from integrals in Multivar calc, what else are useful?

    I want to get a intro to it, can any one give a lecture or link to a intro page? Thanks.
     
  2. jcsd
  3. Nov 28, 2003 #2
    While you're correct that a volume, or area, can be obtained from a single integral, the more general double integral is better suited to more complex problems.

    It allows you to integrate a function over an area, while the triple integral does the same over a volume. There are really an infinite number of applications, but a good one is finding mass from density.

    Using the double integral one can take the density function and integrate it over an area, thus finding the mass of a lamina. With a triple integral, you can find the mass of any relatively simple solid region, for which a density function exists.

    If you'd like to see more about this, I've had good luck here:
    http://www.math.hmc.edu/calculus/tutorials/
     
  4. Nov 28, 2003 #3
    No, you cannot calculate volumes with just one integral, if you are speaking of the volume of an arbitrary-shaped region. (Highly symmetric regions can be reduced to single integrals, because you can implicitly pull out some of the integrals as constants.)
     
  5. Nov 29, 2003 #4
    I was referring to the method of finding volume-using areas of revolution or concentric shells. Which of course does only apply to highly symmetric shapes. I assume this is what you're referring to.
     
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