|Jun10-12, 09:46 PM||#1|
Triple Integrals: Spherical Coordinates - Finding the Bounds for ρ
1. The problem statement, all variables and given/known data
Find the volume of the solid that lies above the cone z = root(x2 + y2) and below the sphere x2 + y2 + x2 = z.
2. Relevant equations
x2 + y2 + x2 = ρ2
3. The attempt at a solution
The main issue I have with this question is finding what the boundary of integration is for ρ. I tried to solve for it by:
I end up getting 0 ≤ ρ ≤ root(2)sinΦ.
However the answer says the 0 ≤ ρ ≤ cosΦ, what am I doing wrong?
|Jun10-12, 10:36 PM||#2|
|Jun10-12, 10:38 PM||#3|
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