1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Volume of a Solid By Revolution

  1. May 28, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the volume of the solid generated by revolving about the line x=-1, the region bounded by the curves y=-x^2 + 4x - 3, and y=0.


    2. Relevant equations
    Shell Method?


    3. The attempt at a solution

    V= 2pi * ∫x* f(x) dx, where a and b are the lower and upper limits of integration, respectively.
    I'm not even sure if what I'm doing is right. And how do I know to use dx or dy? Guidance please?
     
  2. jcsd
  3. May 28, 2013 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Okay
    What does the single x there represent in your shells?
    Hint: if you rotate around x=-1 instead of x=0, you have to change this.
    Do you have constant x or constant y within your shells? That is fine.
     
  4. May 28, 2013 #3
    The x represents the radius, and so I would have to add 1 (- -1)? But I don't even understand what quantity defines the radius here. Is it the -x^2+4x-3? There is no constant given, but I presumed I should use dx since the problem is rotating around the x=-1 line (shift of x-axis left 1 unit).
     
  5. May 28, 2013 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Right.
    The integration variable ("dx") determines that radius.
    The function value (-x^2+4x-3) is the "height" of the shell.
     
  6. May 28, 2013 #5
    So I would end up with

    2 pi * integral sign [(x+1) (-x^2 + 4x-3) dx] ? Is that really it? o.0 I thought it's more intricate.
     
  7. May 28, 2013 #6

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Most problems are easy, if you know how to solve them.
     
  8. May 28, 2013 #7
    Wow, thank you so much mfb. I appreciate it.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Volume of a Solid By Revolution
Loading...