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Understanding minimal substractio for several variables

  1. Sep 8, 2010 #1
    for one dimensional integral [tex] \int_{0}^{\infty}dxf(x) [/tex] i know how to make minimal substraction however for an integral in several variables how is it done ??

    for example for a triple integral

    [tex] \int_{0}^{\infty} \int_{0}^{\infty} \int_{0}^{\infty}dx dy dz f(x,y,z) [/tex]

    i must perfrom

    a minimal substraction in 'x'

    a minimal substraction in 'y'

    a minimal substraction in 'z'

    i know how to make this however what is the following step ?

    a minimal substraction in 'x,y'

    a minimal substraction in x,z

    a minimal substraction in y,z

    a minimal substraction in x,y,z

    this is the part i do not know how to do
     
  2. jcsd
  3. Sep 8, 2010 #2

    mathman

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    What is "minimal substraction"??????
     
  4. Sep 9, 2010 #3
    minimal substraction is that given a divergent integral we must substract some terms to make it convergent.

    for the case of 1 dimension is very VERY easy , the problem is when you have more than one dimension
     
  5. Sep 9, 2010 #4

    mathman

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    One way would be to convert to spherical coordinates. Then the problem would be one-dimensional, since ∞ appears only for the r integral.
     
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