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Homework Statement
By using divergence theorem find the flux of vector F out of the surface of the paraboloid z = x^2 + y^2, z<=9, when F = (y^3)i + (x^3)j + (3z^2)k
Homework Equations
Divergence theorem equation stated in the attempt part
I understand what you mean about the radius changing with z, but how would i integrate dr with limits rmax(z)?Suppose you are doing the z-integral first, so we are looking at a slice of fixed z. Then the slice looks like a disk of radius r_{max}. Instead of 0 to 3, you want to integrate each slice over r from 0 to r_{max}. You can express r_{max} in terms of z.
So you will get
[tex]\int_0^9 \int_0^{r_\mathrm{max}(z)} \int_0^{2\pi} 6 z r \, \mathrm{d}\varphi \, \mathrm{d}r \, \mathrm d{z}[/tex]
where r_{max}(z) depends on z instead of being identically equal to 3 as you have now.