http://i56.tinypic.com/igm0wl.jpg

Printable View

- May 24th 2011, 01:34 PMtransgalacticvolume of half ball mmn 15 4a
- May 24th 2011, 02:04 PMMondreus
I suggest you switch to spherical coordinates as soon as possible. Review the section in your book on spherical coordinates. In particular, you should know how to describe half a sphere and that the Jacobian in spherical coordinates is $\displaystyle J(r, \theta, \varphi)=r^2\sin\theta$. In this case you'll have $\displaystyle 0\leq \theta\leq \pi/2$ (assuming the ball is as you've graphed it).

Spherical coordinate system - Wikipedia, the free encyclopedia - May 24th 2011, 02:58 PMtransgalactic
i tried to solve it like this but i got a bad resolt where is my mistake?

http://i55.tinypic.com/28a14i1.jpg - May 24th 2011, 03:05 PMTheEmptySet
- May 24th 2011, 03:27 PMtransgalactic
where is my mistake why i get 0

- May 24th 2011, 03:40 PMMondreus
TheEmptySet told you where the error lies. I used the symbols from the Wikipedia article where a unit sphere is $\displaystyle 0 < r < 1, 0 < \theta < \pi, 0 < \varphi < 2\pi$.

You have switched the limits for $\displaystyle \theta$ and $\displaystyle \varphi$. - May 24th 2011, 03:47 PMtransgalactic
i disagree

$\displaystyle 0 < \varphi < \pi/2$

not 2 pi

correct? - May 24th 2011, 03:52 PMMondreus
I was referring to the unit sphere.

What you posted is only correct if the Jacobian for the spherical coordinates in this problem is $\displaystyle r^2\sin\varphi$. Again, read the Wikipedia article I linked to if you're confused about the symbols used.