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Math Help - Volume of sphere

  1. #1
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    Volume of sphere

    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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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by cad2blender View Post
    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?
    the function given is not a sphere...

    as for your integral, a substitution of u = \rho^2 would work nicely.
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  3. #3
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by cad2blender View Post
    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?
    Integrating e^{\rho^2}\cdot\rho is just a u-sub. Let u=\rho^2 so \frac{du}{2}=\rho\,d\rho

    \int e^{\rho^2}\cdot\rho\,d\rho=\int\frac{e^u}{2}\,du=\  frac{e^u}{2}=\frac{e^{\rho^2}}{2}
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    EDIT: I'm sorry I meant the integration is e^(rho^2)*(rho^2) that is giving me trouble I forgot to that rho is getting squared. My apologies
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  5. #5
    Super Member redsoxfan325's Avatar
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    That has no closed form expression.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by cad2blender View Post
    EDIT: I'm sorry I meant the integration is e^(rho^2)*(rho^2) that is giving me trouble I forgot to that rho is getting squared. My apologies
    redsoxfan is correct, there is no elementary primitive for that function.

    make sure your integral is set up correctly. perhaps a change of integration order will solve the problem. that is, integrating with respect to another variable other than \rho first may give you a factor you need to get an integrable expression.
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