How Do I Correctly Calculate Volume for a UVZ Coordinate System?

[sedaw]

attached herewith : the problem with my attempt to solve it .

 

[HallsofIvy]

1. What is "an" in "cot ant"?

2. How did you get the limits of integration? Specifically, what are the limits of integration on u and v?

 

[sedaw]

1. What is "an" in "cot ant"?

2. How did you get the limits of integration? Specifically, what are the limits of integration on u and v?

cotan(t) = cos(t)/sit(t)

the limits of integration on u & v simply received from the projection of the region bounded by V on the UV plane -> you can see it circle with radius R=1 .

the limits of integration on z:

you can see in sketch : 0<=z<=U+V (of course just for u & v that in region of the projection )
TNX ...

 

[jackmell]

Yeah, the ant thing . . . not a good way to start sedaw. Did you just enter "cotant" in latex and it partitioned it that way? Just use \cot. But even worst, that picture looks nothing like what I think your V is. Guess the J is Jacobian. But I wouldn't try to change variables until I first tried to solve it the old-fashioned way: just use x, y, and z. Oh, but I would also try to plot a real-looking picture first. Is the volume that part under the paraboloid z=x^2+y^2[/tex] contained by the transparent &quot;square-tube&quot; of x^4+y^4=1 under the paraboloid in the plot below?<br /> <br /> If so, can you see how to arrive at:<br /> <br /> V=8\int_0^{1/2^{1/4}}\int_x^{\sqrt[4]{1-x^4}}\left(x^2+y^2\right) dydx<br /> <br /> That comes out to about 2.22. Would be nice if you already know the answer to see at least if this is on the right track and I realize that&#039;s a tough integral to solve symbolically, but it get&#039;s you grounded at least with something concrete to work with and then perhaps you can use that integral to then change variables. Maybe not though. It&#039;s just a suggestion.

 

[sedaw]

ok.. thank you very much i am appreciate your help.
by the way my picture is V for the uvz axis and not xyz .