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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

    =78.91


    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

    =77.206
     
  2. jcsd
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