1. ## Vector Calculus

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

how do I calculate this integration with vector calculus knowledge?
I think I need to use spherical polar coordinates, but it makes me confuse.

2. Originally Posted by nyammo
let V be the unit ball in three space centered at the origin: 0≦r≦1, find $\ \int\!\!\!\int_Vxdydz\end$
Did you mean $\iiint_{V}dxdydz$ ?

3. no, the equation is collect.
Probably, I need to use Divergence or Stokes' theorem.

4. 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.