Volume of Sphere: Find Integral Solution

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Homework Help Overview

The discussion revolves around finding the volume of a sphere using an integral approach, specifically involving the function f(x,y,z)=e^(x^2+y^2+z^2) within the constraint x^2+y^2+z^2≤9, and utilizing spherical coordinates for the calculation.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to compute the integral but encounters a discrepancy between their result and the expected volume of the sphere. They express uncertainty regarding the integration of e^(rho^2)*rho. Some participants suggest methods such as integration by parts and a substitution approach to simplify the integration process.

Discussion Status

The discussion is ongoing, with participants offering different strategies to tackle the integration challenge. There is acknowledgment of confusion from the original poster, but no consensus has been reached on a specific method or solution yet.

Contextual Notes

The original poster references a known volume formula for a sphere, indicating a potential assumption about the expected outcome versus the integral result. There may be constraints related to the integration process that are not fully explored.

cad2blender
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Find the volume of the sphere:

f(x,y,z)=e^(x^2+y^2+z^2) over x^2+y^2+z^2≤9 using spherical coordinates

After working trough I get this enormous number 228965, when I know its 113.097 using the simple volume formula for a sphere. I think I am having trouble with the integration of e^(rho^2)*rho... Any tips guys?
 
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Integration by parts!
 
You might have better luck with the substitution u=rho2
 
Which is of course correct. Apologies for my confusion.
 

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