I am sorry this question may read a little long, but I really need help with this.

I will thumb up if I get good answer

In looking at iterated integrals and the role of Fubiui's Theorem we have

?01??01?F(x,y)dxdyand?0???0??F(x)x+y1?f(y)dxdy

eg calculation in the first quadrant where we have to consider both singular behavior at the origin and decay at infinity and for the second integral having f to be a square integrate function which is?0???f(x)?2dx?

We want to explore simple extensions from the product space[0,?][0,?] (in first quadrant) toR2R2 andR3R3

Consider the integral

I2?=??R2R2?1+?x?21???x?2+?y??21??1+?y??21?dxdy

Where x=(x1?,x2?), y?=(y1?,y2?),dx=dx1?dx2?,dy=dy1?dy2?

1.Show that using earlier calculation, we can find the value ofI2?

But the problem is not the same inR3