Originally Posted by

**Dubulus** i have an idea on how to solve this problem, but it seems like itd be way too much work to even be possible...

triple integral over R of dV / (x^2 + y^2 + z^2)

where R is the region between:

x^2 + y^2 + z^2 = 1

x^2 + y^2 + z^2 = 4

am i correct in thinking that first i have put convert to spherical coordinates and then insert pdpdthetadphi?

ps how do you insert the integral symbol and all that fun stuff?

I'll answer your last question first. We use LaTeX here at the forums.

As I answer you're problem, I'll show what code was used.

So we are to integrate $\displaystyle \iiint\limits_G x^2+y^2+z^2 \,dV$?

Code:

[tex]\iiint\limits_G x^2+y^2+z^2 \,dV[/tex]

Note that the region is defined as the area between two circles [when looking down at the xy plane]

So our limits for the radius would then be from 1 to 2.

The best coordinate system to use would be the spherical coordinate system. We see that $\displaystyle \varrho$ is defined between 1 and 2.

$\displaystyle \varphi$ would be defined between 0 and $\displaystyle \pi$

$\displaystyle \vartheta$ would be defined between 0 and $\displaystyle 2\pi$

So our triple integral would be $\displaystyle \int_0^{2\pi}\int_0^{\pi}\int_1^2 \varrho^4\sin\varphi \,d\varrho\,d\varphi\,d\vartheta$

Code:

[tex]\int_0^{2\pi}\int_0^{\pi}\int_1^2 \varrho^4\sin\varphi \,d\varrho\,d\varphi\,d\vartheta[/tex]

Does this make sense?

--Chris