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Tom2
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Homework Statement
To integrate a function (the function itself is not important) over the region Q. Q is bounded by the sphere x²+y²+z²=2 (ρ=sqrt2) and the cylinder x²+y²=1 (ρ=cscφ).
To avoid any confusion, for the coordinates (ρ,φ,θ), θ is essentially the same θ from polar coordinates in 2 dimensions while φ is the angle measured from the +z axis to ρ.
Homework Equations
Jacobian = ρ²sinφ
The Attempt at a Solution
I can see that the limits for ρ go from cscφ to sqrt2.
Also θ should go from 0 to 2pi.
But I'm not sure how to find the limits for φ (the book says it goes from pi/4 to 3pi/4). How is it justified?
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