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

  1. Oct 20, 2014 #1
    1. The problem statement, all variables and given/known data
    Proper way to graph xy = 1 for a Cylindrical Shell problems.

    2. Relevant equations

    V = ∫^b_a 2πy f(y) dy

    3. 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?
     
  2. jcsd
  3. Oct 20, 2014 #2

    vela

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    They aren't different. Why do you think they are?
     
  4. Oct 20, 2014 #3
    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?
     
  5. Oct 20, 2014 #4

    vela

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    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.
     
  6. Oct 20, 2014 #5
    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.
     
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