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I have this doubt that I cannot solve. $\int \limits_{D}\dfrac{|x−1|^a}{|x^2−y^2|^b} \, dx \, dy$ where $D=\{(x,y)\in \mathbb{R}^2: x^2+y^2<1\}$ If I use polar coordinates I cannot solve anything. Could you help me? Thank you

Daniel Fischer
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maxandri
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1 Answers1

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The $r$ integral in polar coordinates can be solved analytically. It is of the form

$$C\int_{r=0}^1\frac{(\alpha r^2+\beta r+\gamma)^a}{r^{2b}}rdr$$

After that it depends on specific properties of $a$ and $b.$

Justpassingby
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  • Sorry, but in the denominator I have $x^2 - y^2$ and not $+$. So how can I find $r^2$? $x-1$ should become $r\cos(\theta)-1$, which substitution do you use? – maxandri Dec 12 '15 at 17:37