1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Solids of Revolution - Volume

  1. Feb 7, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the volume of the solid obtained by rotating the region bounded by y=2x2-x3 and y=0 about the y-axis

    2. Relevant equations

    There no required method (between Disk, Washer, Shell). In my attempt below, I used the Shell method, I believe. 2π(shell radius)(shell height)dx

    3. The attempt at a solution

    I graphed the equation and ended up with V = ∫20 2π(x)(2x2-x3)dx

    V =2π*limit 0 to 2* (2x3-x4)dx

    V = 2π *limit 0 to 2* x4/2 - x5/5

    V =[tex]2π (1/2 - 1/5)[/tex]
    V= 3π/5

    Am I on the right track or did I mess up horribly in the setup? I feel like the area where I might have made a mistake was the limits I set... and still getting used to the functions on here lol sorry
  2. jcsd
  3. Feb 7, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper

    The setup looks ok to me but it looks like you are putting x=1 for the upper limit of your integral instead of x=2 when you evaluate it. Why would you do that?
    Last edited: Feb 7, 2012
  4. Feb 8, 2012 #3
    Ah, just a silly error. So when I plug in 2 for x rather than one. I get 8 - 6.4 = 3.2pi. But other than that it looks alright? I was worried about how I choose to set up my limits since I found the x intercept for the upper limit...but kinda sorta just guessed that the other was 0. There has to be a more technical way to go about that. @_@
  5. Feb 8, 2012 #4


    User Avatar
    Science Advisor
    Homework Helper

    Yes, that's fine. There are two x intercepts. Factor. 2x^2-x^3=x^2*(2-x)=0. So either x=0 or x=2.
  6. Feb 8, 2012 #5
    Thanks so much!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook