That would be r = (cosθ-π/2).
So I guess you could say that ρ is equal to (sinφ-π/2)
So the integral would be as follows:
∫0→π/2 ∫0→π/2 ∫sinθ-π/2→π/2 f(ρ,φ,θ) ρ^2 sinφ dρdφdθ ?
Thanks for the note about the convention of what θ indicates. I'll keep that in mind in the future but I'll stick with what I've been doing right now for the sake of consistency.
I tried to define the smaller sphere in terms of ρ, φ, and θ:
x^2 + y^2 + (z+1)^2 = 1
x^2 + y^2 + z^2 + 2z + 1 = 1...
I do understand the concept of an integral, I just don't understand how you can adequately describe what seems to need 4 bounds with 2 bounds. For example, at ρ extends from 0 to the lower edge of the small sphere. Then, ρ extends from the upper edge of the small sphere to 2. Here, I cannot say...
Thanks for your reply. Drawing a projection onto the yz-plane did help me visualize the problem; what remains confusing is the bounds of ρ for 0 ≤ φ ≤ ≈ 26°. In these cases, is ρ considered to be the sum of the distance from the origin to the small sphere and the distance from the other side of...
Homework Statement
The problem asks for a single triple integral (the integrand may be a sum but there must be a single definition for the bounds of the integral) representing the volume (in the first octant) of the shell defined by a sphere of radius 2 centered around the origin and a sphere...
Hey PF, I'm a physics major at Vanderbilt University studying basic Electricity and Magnetism. I love physics because it offers me a deeper understanding of my surroundings, and the problem solving is probably good for me too. I hope to take my studies to space as an astronaut, or maybe research...