I find this to be a very tough problem:(adsbygoogle = window.adsbygoogle || []).push({});

1) Determine whether the improper integral I

∞ ∞

∫ ∫ [sin (x^{2}+ y^{2}) / ln(x^{2}+ y^{2})] dxdy

2 2

converges or diverges.

All I can think of and try is by changing it to polar coordinates:

I=A+B where

A=

pi/4--- ∞

∫ ----- ∫ [sin (r^2) / ln(r^2)] r dr(dtheta)

2 -- 2/sin(theta)

B=

pi/2 -------∞

∫---------- ∫ [sin (r^2) / ln(r^2)] r dr(dtheta)

pi/4 ---2/cos(theta)

But how can I show that each of them converges (or diverges)?

Can someone please help me out? Thank you!

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# Homework Help: Improper Multiple Integrals (2)

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