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Question Number 30741 by abdo imad last updated on 25/Feb/18

l e t g i v e D = R_{+}^{2} - {(0, 0)} a n d α f r o m R l e t

C_{1} = {(x, y) \in D / 0 < x^{2} + y^{2} ⩽ 1}

C_{2} = {(x, y) \in D / x^{2} + y^{2} ⩾ 1} s t u d y t h e c o n v e r g e n c e o f

I = \int \int_{C_{1}} \frac{d x d y}{{(\sqrt{x^{2} + y^{2}})}^{α}} a n d J = \int \int_{C_{2}} \frac{d x d y}{{(\sqrt{x^{2} + y^{2}})}^{α}} .