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: Volume by Cylindrical shells

  1. Feb 14, 2012 #1
    1. The problem statement, all variables and given/known data

    Rotate around the y-axis the region above the graph of y=x3 that is bounded by the lines x=1 and y=8

    2. Relevant equations

    dV= (2pix)(y)(dx)

    3. The attempt at a solution

    dV = (2pix)(y)dx
    dV = (2pix)(x^3) dx
    = 2pix^4

    I integrated from y = 1 to y=8 and I get the wrong answer.

    V = 2∏x=1x=2x^4 dx
    V = 2∏[1/5x^5]21

    Can someone please explain to me, how I would set up this equation? Something to do with the first function subtracting the second function which I think is x=1

    Here is a graph: http://www3.wolframalpha.com/Calculate/MSP/MSP15491a07c8557bi4590b00001ibd52eb6gcc3177?MSPStoreType=image/gif&s=21&w=366&h=298&cdf=RangeControl [Broken]
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Feb 14, 2012 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    The problem is with the following:
    dV= (2πx)(y)(dx)
    The height of the cylindrical shell is 8-y, not y.

    So dV = (2πx)(8-y)(dx)
    Last edited by a moderator: May 5, 2017
  4. Feb 14, 2012 #3

    [STRIKE]So dV = (2∏x)(8-x^3)dx
    = 16∏x-2∏x^4 dx

    V= 2∏∫(8x-x^4) dx ?


    Thank you for helping me!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook