Easy Integration: Finding Flux of a Sphere Surface | Double Integral Help

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SUMMARY

The discussion focuses on calculating the double integral of the function (x^2 - y^2 + 2) over the region defined by the constraint x^2 + y^2 ≥ 2, while also finding the flux of a sphere defined by x^2 + y^2 + z^2 = 9. The user initially attempts Cartesian coordinates but finds it overly complex and shifts to parametrization. The bounds for the integral are identified as t ranging from 0 to 2π and r starting from √2, but the upper bound remains unclear. Ultimately, the discussion concludes that the integral diverges when integrating over specific regions.

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Homework Statement


I want to perform the following integration:
double integral of [(x^2)-(y^2)+2] dxdy where the function is subjected to the bound (x^2)+(y^2) greater than or equal to 2.

I'm trying to find the flux of a surface of a sphere (x^2)+(y^2)+(z^2)=9.

Homework Equations


Nothing, just rules of integration.

The Attempt at a Solution


Using Cartesian coordinates seems far too difficult. I could show you my work, but it's messy and complicated.
If I use parametrisation, then I get
double integral of [(r^2)cos^2(t)-(r^2)sin^2(t)+2) rdrdt
what are the bounds though?
t is between 0 and 2pi I'm pretty sure, but what about r?
It seems difficult since x^2+y^2 is greater than or equal to 2. This means that r^2 is greater than or equal to 2. Thus, it seems sqrt(2) is a lower bound, but what would the upper bound be?

Does this make any sense?
 
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For the trig part: Hint: http://www.sosmath.com/trig/Trig5/trig5/trig5.html
However, considering the bound you stated, it looks like your integral diverges.
If you integrate only where x>2 and y<1, you already get divergence.
So, to answer your question: No.
 
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