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Integrating to find average value

  1. May 30, 2012 #1
    I have the function:
    f(x,y)= x*(y^2)*e^-((x^2+y^2)/4), with x and y from -3 to 3
    I took the integral of this function and got 0 as my answer.
    I need to find the average value, which is 1/area multiplied by the double integral. Since the double integral is 0, would the average value also be equal to 0?
    How would I solve this?
     
  2. jcsd
  3. May 31, 2012 #2

    sharks

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    What is the whole question?
     
  4. May 31, 2012 #3

    SammyS

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    Yes, that integral is zero.

    If this is a problem you have been given to work on, Please, give us the entire problem, word for word, as it was given to you.

    I see that sharks beat me to the punch !
     
  5. May 31, 2012 #4
    The whole question is to find the average value of
    f(x,y)= x*(y^2)*e^-((x^2+y^2)/4), with x and y from -3 to 3

    In my textbook the formula given to find it is
    (1/Area)*∫∫f(x,y)
    I took the double integral and found that the answer is 0.
    The area would be 36, since both x and y are from -3 to 3.
    1/36 * 0 = 0
    Can the average value really be 0 though?
     
  6. May 31, 2012 #5

    SammyS

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    Yes! Why not ?
     
  7. May 31, 2012 #6
    Notice it is an odd function when viewed from the x-axis. Try graphing it in wolfram alpha.
     
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