- #1
Change of varibles in integrals (More than 1 question)
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Homework Help Overview
The discussion revolves around the topic of change of variables in integrals, particularly in the context of spherical coordinates. Participants are exploring the integration limits and the implications of these limits on the integration process.
Discussion Character
- Exploratory, Assumption checking, Problem interpretation
Approaches and Questions Raised
- Some participants question the appropriateness of integrating \(\theta\) from 0 to \(2\pi\) and \(\varphi\) from 0 to \(\pi\), suggesting this might also represent a sphere. Others express uncertainty about integrating specific functions and the limits involved.
Discussion Status
Participants are actively discussing the limits of integration and the setup of the integrals. Some guidance has been offered regarding the limits for \(\theta\) and the relationship between variables, but no consensus has been reached on the correct approach.
Contextual Notes
There are references to specific functions and density definitions that may not be fully clarified, as well as potential misunderstandings about the integration limits for the given problems.
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SammyS
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athrun200 said:
For 0 < θ < π sin θ is positive, for π < θ < 2π sin θ is negative.
- #4
SammyS
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For (d) : You have the wrong limits for the θ integration.athrun200 said:Homework Statement
I have questions on d and e
I don't know how to integrate these functions
Also, the density is given by ρ = M π a2, where M is the mass of the circular lamina and assumes that ρ is the mass per unit area.
For (e): Your integral has both r & θ in it.
I suggest using r = 2a cos (θ) to find dr/dθ . What are the limits of θ for this integral ?
Last edited:
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