Subject: Re: Integration in Spherical Coordinates of a cube
Date: Sun, 17 Nov 1996 21:30:06 -0500
From: Alex Bogomolny
The problem you have stems from the first constraint:
0 < theta < Pi/4
which is wrong. To see this, look at the vertical triangle in the plane x=y between z=0, y=1/2 and y=z. This is one side of the pyramid whose volume you correctly estimate as 1/24. In this triangle tan(theta)=1/sqrt(2) so that theta is not Pi/4!
From a different viewpoint, the equation theta=Pi/4 does not define a plane. It's a cone hence different from the plane y=z.
With best wishes,