Volume enclosed by a cone and a plane

[thonwer]

Homework Statement

Find the volume enclosed by the cone x^{2}+y^{2}=z^{2}
and the plane 2z-y-2=0.

Homework Equations

\int\int\int dV

The Attempt at a Solution

In the image Cono=Cone and Plano=Plane

 

[Mark44]

Problems about integration should be posted in the Calculus & Beyond section, not in the Precalculus section. I have moved your post.

 

[thonwer]

I have tried to solve it in a different way but I do not think it is much better. Can anybody help me?

 

[LCKurtz]

For what it's worth, I don't see anything obviously wrong with your work. I entered the $r,\theta$ integral you get into Maple and it just hung trying to solve it. I doubt you are going to find an elementary solution.

 

[thonwer]

For what it's worth, I don't see anything obviously wrong with your work. I entered the $r,\theta$ integral you get into Maple and it just hung trying to solve it. I doubt you are going to find an elementary solution.

So my first attempt is OK? Because I'm finding troubles with the absolute value of (y) and (-y). I'm not sure if everything I've put is correct.

 

[LCKurtz]

I didn't check your rectangular coordinate version. The $r,\theta$ change of variables you used would be the natural way to set it up and that's all I looked at.

 

[thonwer]

I didn't check your rectangular coordinate version. The $r,\theta$ change of variables you used would be the natural way to set it up and that's all I looked at.

If you do not mind could you please take a look at my rectangular coordinate version?