Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let be an interal on $ \mathbb{R}^{n} $ in the form

$$ \int_{R^{n}}dV \frac{P(x_1,x_2,\dots,x_n)}{Q(x_1,x_2,\dots,x_n)}$$

which is divergent.

My question is: Could we substract from this integral a polynomial of the form

$$ K(x_1,x_2,..,x_n) $$ such that the integral

$$ \int_{R^{n}} \left(\frac{P(x_1,x_2,\dots,x_n)}{Q(x_1,x_2,\dots,x_n)}-K(x_1,x_2,x_3,\dots,x_n)\right)dV$$

is now finite?

For the case of a single variable I know how to do it but for multivariable calculus I do not know if this can be done, thanks.

This polynomial $$K(x_1,x_2,x_3,\dots,x_n)$$ can also include inverse power terms for example $ (x_2+1)^{-1}x_3 $ or $ ((x_1+2)(x_2+3))^{-1} $, Laurent polynomials.

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.