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: Revolution about horizontal and vertical lines

  1. Jan 20, 2014 #1
    1. The problem statement, all variables and given/known data

    Use shell method to find volume.
    rotate about the x-axis

    2. The attempt at a solution

    I cannot seem to solve this. I thought this was the way to solve it, but I don't understand if I am missing something crucial.
    This is how I set up the integral.

    v=integral from 1 to 4 (2pi* y * (y-2-sqrt(y))
    This is not giving me the correct answer. Is this that way to set this up?
    I also tried the same integral from 0 to 4, and cannot determine what I am doing wrong.
    I would appreciate any help.
    Last edited: Jan 20, 2014
  2. jcsd
  3. Jan 20, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper

    hi cathy! welcome to pf! :smile:
    let's see … you're using cylindrical shells of radius y, thickness dy, and length x2 - x1

    and that should be between where they meet, at (0,0) and at (2,4): ie for y between 0 and 4

    so you second try should work …

    can you show us your calculations? ​
  4. Jan 20, 2014 #3
    well, i tried the second one again, like you said, and here are my calculations:

    taking the antideriv of,
    antideriv would be:
    1/3y^3 - y^2 - 2/5y^5/2
    plugging in 4, I get
    64/3 -16 -64/5 = -112/15 *2pi
    = -224/15pi
    and that is not correct

    Did I do something wrong here? Please advise.
  5. Jan 21, 2014 #4


    User Avatar
    Science Advisor
    Homework Helper

    (just got up :zzz:)

    looks ok (apart from everything being minus what it should be, since x2 > x+2) :confused:

    have you tried +224/15π ?
  6. Jan 21, 2014 #5
    Ohh. i actually see the problem. since it's required for me to do shells, the problem needed to be divided into two separate integrals.
    thank you for your help tiny-tim :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted