1. Originally Posted by TriKri
I guess you mean indefinite multi-dimensional integral. Yes, this was only for the rectangular case, you are right. An arbitrary surface can be varied in an infinite numbers of ways (it can be extended in an infinite number of edge points), hence I believe that it's difficult to find a primitive function from which an integral over an arbitrary surface easily can be expressed, withouth using at least one more integral. And of course it doesn't become easier to find a primitive function which makes any sense when the dimension of the integral increases even more.
Yes you are right it was a typo
As I had some integrals that in my computer can not be calculated (not linear, multivariate polynomials)... I thought might be easier to use some scrap paper and hard-code the results inside my code...
Then I can convert the integrals into simple functions of the boundaries.
You can check below what I mean
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2. In your case it seems like the function F(x, y) (taken from my example) is = (x^2*y^2)/4. Then you insert the limits like I did in my example to get the same expression as you have on the bottom of your paper.

3. Originally Posted by TriKri
In your case it seems like the function F(x, y) (taken from my example) is = (x^2*y^2)/4. Then you insert the limits like I did in my example to get the same expression as you have on the bottom of your paper.
This was just a toy-model : My equations are bivariate polynomials of order >2... and thus I think I should try to convert them into F(a,b,c,d) as me and you show in our examples. Then I do not need to run any integrate calculation using R or Matlab as I only do have simple functions that I need to call with the right arguments.

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