Proper way to graph xy = 1 for a cylindrical shell problem

[Eddie10]

Homework Statement

Proper way to graph xy = 1 for a Cylindrical Shell problems.

Homework Equations

V = ∫^b_a 2πy f(y) dy

The Attempt at a Solution

I am rotating around the x-axis, so I am integrating with respect to y, but should I choose x = 1/y, or y = 1/x to solve my problem?

How are these two functions different? x = 1/y and y = 1/x different?

 

[vela]

They aren't different. Why do you think they are?

 

[Eddie10]

They aren't different. Why do you think they are?

Well, if I am integrating with all y variables, shouldn't it make sense to use x = 1/y, instead of y = 1/x, so the variables match? For example, v = 2pi (Integrand Sign) f(y) dy.

Or, in this case, does the variables used not affect the answer once integration is applied?

 

[vela]

Yes, of course. You need the integrand to be in terms of $y$ if you're integrating with respect to $y$. Isn't this always the case? I guess I'm not sure why you'd think you could use 1/x in this case.

 

[Eddie10]

Yes, of course. You need the integrand to be in terms of $y$ if you're integrating with respect to $y$. Isn't this always the case? I guess I'm not sure why you'd think you could use 1/x in this case.

Yeah, I was double checking to make sure I couldn't use 1/x in this case, since I am integrating everything for "dy" instead of "dx".

Thanks.