LCKurtz said:
You're getting worse, not better.
Look in your post #7. The upper limit for ##z## is not ##1##. Nor is ##r=1## correct for its upper limit. And why the extra ##r##?
And the upper limit for ##z## isn't ##r## either. And its lower limit isn't ##r/2##. And the upper limit for ##r## isn't ##1##. Perhaps you should just start over.
the extra r came simply from a heuristic approach, it seemed correct.
starting over:first thing converting over to cylindrical
##0 \le \theta \le 2\pi## this one I see no issues with
I have ##x^2+y^2+z^2 \le 1##
this is where I wasn't sure about converting, do I treat ##z^2## just as is or treat it as ##z^2=x^2+y^2##
the first way of treating z
##r^2cos^2(\theta) + r^2sin^2(\theta) + z^2 =1## but graphing this is not the same sphere, it
the second way
##r^2cos^2(\theta) + r^2sin^2(\theta) + (r^2cos^2(\theta) + r^2sin^2(\theta)) =1## but in order for this to be the same sphere it has to be equal to 2 or I take out ##(r^2cos^2(\theta) + r^2sin^2(\theta))## and keep it set as equal to 1
some explanation on this would be appreciated immensely
now for the r and z bounds
##\frac{1}{2} \le z \le \sqrt{1-x^2-y^2}## this does not work if put as ##\frac{1}{2} \le z \le \sqrt{1-r^2cos^2(\theta)-r^2sin^2(\theta)}##
this can't be that difficult but I am missing something
EDIT: also doing it in rectangular I graphed my x,y bounds and those aren't any good either, only way I could get the proper bounds was to have each of x,y,z in terms of the other two.