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Math Help - Vector Calculus

  1. #1
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    Vector Calculus

    let V be the unit ball in three space centered at the origin: 0≦r≦1, find
    \<br />
\int\!\!\!\int_Vxdydz<br />
\end

    how do I calculate this integration with vector calculus knowledge?
    I think I need to use spherical polar coordinates, but it makes me confuse.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by nyammo View Post
    let V be the unit ball in three space centered at the origin: 0≦r≦1, find \ \int\!\!\!\int_Vxdydz\end
    Did you mean \iiint_{V}dxdydz ?
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  3. #3
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    no, the equation is collect.
    Probably, I need to use Divergence or Stokes' theorem.
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  4. #4
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    No, it is not correct- what you wrote makes no sense. You cannot have a double integral over a three dimensional body. You need to integrate either over the unit ball or over the unit sphere (the surface of the unit ball).

    In either case, because the region is symmetric while the integrand, x, is an odd function, the integral is 0.
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