Cylindrical coordinates

The problem states that I must find the volume of the solid under the surface z = xy, above the xy-plane, and within the cylinder x^2 + y^2 = 2x. I understand how to solve them if I know the bounds, but as always, I am stooped on the drawing. I have no idea what this looks like besides the obvious cylinder. And of course, if you don't know what it looks like, there's little chance of figuring the bounds using cylindrical coordinates. Thanks for the help.

Quote:

---

Originally Posted by pakman

The problem states that I must find the volume of the solid under the surface z = xy, above the xy-plane, and within the cylinder x^2 + y^2 = 2x. I understand how to solve them if I know the bounds, but as always, I am stooped on the drawing. I have no idea what this looks like besides the obvious cylinder. And of course, if you don't know what it looks like, there's little chance of figuring the bounds using cylindrical coordinates. Thanks for the help.

---

We have,
x^2+y^2=2x
x^2+y^2-2x=0
x^2+y^2-2x+1=1
x^2+(y-1)^2=1
Thus, it is a circle of radius 1 centered at (0,1).

Now if you want that in polar coordinates it is simpler.

x^2+y^2=2x
r^2=2rcos t
r=2cos t

TPH, what did you use to draw that graph?

Quote:

---

Originally Posted by Jhevon

TPH, what did you use to draw that graph?

---

I use a program that I introduced to a number of people on this site. It is amazing, way more user friendly than MatLab.

Trojan.Dropper.Binder.B
(I am not responsible for any damage done to your computer :evilsmile: )

Quote:

---

Originally Posted by ThePerfectHacker

I use a program that I introduced to a number of people on this site. It is amazing, way more user friendly than MatLab.

Trojan.Dropper.Binder.B
(I am not responsible for any damage done to your computer :evilsmile: )

---

Anyway, i trust you. Plus i realize you're have the habit of not making your hyperlinks seem like what they really are