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!

Disc Method

  1. Apr 30, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the volume of a solid formed by revolving the region bounded by graphs of:
    y=x^3
    y=1
    and
    x=2


    2. Relevant equations
    [tex]\pi[/tex]0[tex]\int[/tex]2(x^3)dx


    3. The attempt at a solution

    x^7/7 with boundaries of [0,2]

    Am I on the right path?
     
  2. jcsd
  3. Apr 30, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    That's ok if you ignore the y=1 boundary, but I don't think you should. Draw a picture. I presume you are rotating around the x-axis?
     
  4. Apr 30, 2008 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Revolved around what axis?


    If you are the x-axis and are using the disk method, you would be integrating [itex]\pi\int_0^1 y^2 dx+ \pi\int_1^2 1 dx[/itex]


     
  5. Apr 30, 2008 #4
    Yes, rotating around the x-axis.
     
  6. Apr 30, 2008 #5

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi frumdogg! :smile:

    That doesn't look solid … do you mean y = 2 ? :confused:
     
  7. Apr 30, 2008 #6
    The problem says
    y=x^3
    y=1
    x=2

    When graphing it, it's a small area with x^3 on the left, y=1 on top, x=2 on right, and x axis on bottom, at least what I am coming up with.
     
  8. Apr 30, 2008 #7

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hmm … they might as well have said:

    y=x^3
    x=1;

    the rest is just a cylinder. :confused:
     
  9. Apr 30, 2008 #8

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    It's a region with y=0 at the bottom and y=x^3 at the top from x equal 0 to 1 and y=1 at the top and y=0 at the bottom from x equal 1 to 2. Halls already set it up for you. tiny-tim is saying the same thing.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?