Volume of Sphere: Find Integral Solution

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The discussion focuses on calculating the volume of a sphere using the function f(x,y,z)=e^(x^2+y^2+z^2) over the constraint x^2+y^2+z^2≤9. The user initially arrives at an incorrect volume of 228965 due to difficulties in integrating e^(rho^2)*rho. The correct volume, 113.097, is derived using the standard volume formula for a sphere. The conversation highlights the importance of integration techniques, specifically integration by parts and the substitution method u=rho^2, to resolve the integration challenges.

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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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