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Average value of function

  1. Feb 2, 2009 #1
    To find the average value of a function of one variable, you integrate it and multiply it by 1/(b - a) , where b and a are the limits of integration , uper and lower, respectively.

    But how does one do this for a function of two variables, defined on a rectangle?
     
  2. jcsd
  3. Feb 2, 2009 #2

    Dick

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    The same way, basically. Integrate the function over the rectangle and divide by the area of the rectangle.
     
  4. Feb 3, 2009 #3
    Thanks.

    Well I am trying a question. The integrand is (x^2)y. The domain is [2,4] * [-6,6].

    Now when I integrate it with respect to y first, it goes to zero. It does not go to zero when you start with x. How is this possible?
     
  5. Feb 3, 2009 #4

    gabbagabbahey

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    Bad math. :wink:....It should be zero in both cases, try showing us what you are doing when you integrate it over x first....:smile:
     
  6. Feb 3, 2009 #5
    Possibly!:biggrin:

    Ah I see what I've been doing wrong! I don't even need to work out the average value, since it integrates to zero, as it should, since it is evenly distributed in the positve and negative y areas!
     
    Last edited: Feb 3, 2009
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