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supermiedos
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Homework Statement
Find the mass of the solid bounded from above z = √(25 - x2-y2) and below from z = 4, if its density is δ = k(x^2 + y^2 + z^2)^(-1/2).
Homework Equations
m = ∫∫∫δdV
The Attempt at a Solution
The plane z = 4 is transformed into ρcosφ = 4, that is, ρ = 4secφ. And x^2 + y^2 + z^2 = 25 is ρ = 5. θ goes from 0 to 2π. But I'm struggling finding the limits for φ (the azimuth). I think φ must go from 0 to π/2, but I can't get the correct answer (which is kπ). The book suggests that I must express the upper limit for φ as an inverse cosine, but why is that? From the figure I can see φ goes from 0 to 90°.
Thanks in advance