1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Shell method

  1. Mar 26, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the volume of the solid of revolution:
    F(x)=2x+3 on [0,1]
    Revolved over the line x=3 and y=5

    2. Relevant equations
    Shell Method: 2[tex]\pi[/tex][tex]\int[/tex][tex]^{b}[/tex][tex]_{a}[/tex]x[f(x)-g(x)]dx
    obviously just sub y for dy
    Disk Method: [tex]/pi[/tex][tex]/int[/tex][tex]^{b}[/tex][tex]_{a}[/tex][F(x)[tex]^{2}[/tex]-G(x)[tex]^{2}[/tex]dx

    3. The attempt at a solution
    line x=3: 2[tex]/pi[/tex][tex]/int[/tex](3-x)(2x+3)dx =115.19

    answer key is unfortunately in disk method which I don't like as much:
    [tex]/pi[/tex][tex]/int[/tex][tex]^{3}[/tex][tex]_{0}[/tex](9-4)dy + [tex]/pi[/tex][tex]/int[/tex][tex]^{5}[/tex][tex]_{3}[/tex](3-((y-3)/2))[tex]^{2}[/tex]-4dy


    line y=5: 2[tex]/pi[/tex][tex/int[/tex][tex]^{5}[/tex][tex]_{0}[/tex](5-y)(1-((y-3)/2)) =130.8996

    answer key/ disk method: [tex]/pi[/tex][tex]/int[/tex][tex]^{1}[/tex][tex]_{0}[/tex](25-(5-(2x+3))[tex]^{2}[/tex]dx

  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted