Recent content by Stirling Carter

Thanks for all of your help! I will learn LaTeX before posting here again.

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 ?

Wouldn't ρ be the same for every fixed φ regardless of θ?

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...