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## Main Question or Discussion Point

i want to compute the integral

[tex] \iint_{D} f(x,y)dxdy [/tex] here f(x,y) is a Rational function and the integral is DIVERGENT.

in order to regularize i had the following idea , i introduce a regulator

[tex] \int_{D} \frac{f(x,y)}{(x^{2}+y^{2}+1)^{s}}dxdy [/tex] so for big 's' the integral is convergent

i make now a change of variable to polar coordinates so

[tex]g(r)= \int_{\theta}f(r, \theta) [/tex]

then the initial intengral becomes (after integration over the angular variable, this integraiton can be made by either numerical or exact analytic methods)

[tex] \int_{0}^{\infty} \frac{f(r ,\theta)}{(r^{2}+1)^{s}}rdr = I(s) [/tex]

then this integral is easier to handle, i use tables to compute it and then to analytically continue with external parameter 's' to s =0 in order to botain a regularization of the initial integral

however my teachers say this can not be done how is it possible ¿¿ are they cheating me ?

[tex] \iint_{D} f(x,y)dxdy [/tex] here f(x,y) is a Rational function and the integral is DIVERGENT.

in order to regularize i had the following idea , i introduce a regulator

[tex] \int_{D} \frac{f(x,y)}{(x^{2}+y^{2}+1)^{s}}dxdy [/tex] so for big 's' the integral is convergent

i make now a change of variable to polar coordinates so

[tex]g(r)= \int_{\theta}f(r, \theta) [/tex]

then the initial intengral becomes (after integration over the angular variable, this integraiton can be made by either numerical or exact analytic methods)

[tex] \int_{0}^{\infty} \frac{f(r ,\theta)}{(r^{2}+1)^{s}}rdr = I(s) [/tex]

then this integral is easier to handle, i use tables to compute it and then to analytically continue with external parameter 's' to s =0 in order to botain a regularization of the initial integral

however my teachers say this can not be done how is it possible ¿¿ are they cheating me ?