Finding the Mass of a Solid in 3d

  • Thread starter c.dube
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  • #1
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Homework Statement


Find the mass of the solid bounded by the cylinder [itex]x^2+y^2=2x[/itex] and the cone [itex]z^2=x^2+y^2[/itex] if the density is [itex]\delta = \sqrt{x^2+y^2}[/itex]

[b2. The attempt at a solution[/b]
I had some trouble looking at how to set up the limits on this integral. What I came up with was:
[itex]2 \int_0^2 \int_0^{\sqrt{2x^2+2x}} \int_0^{\sqrt{x^2+y^2}} \sqrt{x^2+y^2} dzdydx [/itex]
[itex]= 2 \int_0^2 x^2\sqrt{x^2+y^2} + ((\sqrt{x^2+y^2})^3)/3 dx[/itex]
And this is just an ugly integral. I tried doing it in cylindrical coordinates but it wasn't working out terribly well that way either. Any hints? Thanks!
 

Answers and Replies

  • #2
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Nevermind, I got an answer. Can anyone confirm [itex]6\pi[/itex]?
 

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