- #1
robertjford80
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Homework Statement
I'm just interested in knowing where the 4 comes from in front of the integral.
Measuring volume of spheres using triple integrals
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Homework Help Overview
The discussion revolves around understanding the use of a factor of 4 in the context of evaluating triple integrals for measuring the volume of spheres. Participants are exploring the reasoning behind this factor and its relation to the limits of integration.
Discussion Character
- Conceptual clarification, Assumption checking
Approaches and Questions Raised
- Participants are questioning the origin of the factor of 4 and discussing the integration limits, particularly the choice of integrating from 0 to π/2 versus 0 to 2π. There is an exploration of the implications of circular symmetry in the integration process.
Discussion Status
The discussion is active, with participants providing insights into the reasoning behind the integration limits and the factor of 4. There is a recognition of the circular symmetry in the problem, but no explicit consensus has been reached regarding the best approach.
Contextual Notes
Some participants note potential confusion in the notation used for the integral limits, suggesting that the representation may lead to misunderstandings.
I'm just interested in knowing where the 4 comes from in front of the integral.
- #2
tiny-tim
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hi robertjford80! 
that 4∫0π/2 is really ∫02π …
i suppose the writer thought it looks confusingly like ∫00, though i see nothing wrong with it!
that 4∫0π/2 is really ∫02π …
i suppose the writer thought it looks confusingly like ∫00, though i see nothing wrong with it!
- #3
robertjford80
- 388
- 0
Ok, pretty unexpected but I guess it makes sense.
- #4
HallsofIvy
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In other words, they are using the circular symmetry of the figures, integrating from 0 to [itex]\pi/2[/itex], rather than from 0 to [itex]2\pi[/itex], then multiplying by 4.
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