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Area of Surface of Revolution

  1. Aug 3, 2009 #1
    1. The problem statement, all variables and given/known data
    Find area of surface generated by revolving about x-axis.

    y=x^3/3 1<=x<=sqrt(7)


    2. Relevant equations
    find f'(x) = x^2

    3. The attempt at a solution

    A = integral[ (x^3/3) * [(1+(x^2)^2] ^(1/2) ] ]dx
    = integral[ (x^3/3) * [(1+x^4) ^(1/2) ]dx
    I just don't know where to go from here.

    Any help is appreciated,
    Thank You.
     
  2. jcsd
  3. Aug 3, 2009 #2

    Mark44

    Staff: Mentor

    Ordinary substitution: let u = 1 + x^4.

    I'm assuming that you have the correct integrand. If so, this substitution will help you out.
     
  4. Aug 3, 2009 #3
    You forgot the [tex]2\pi[/tex] in your equation, but you probably have that on paper. Here's what the integral should look like.

    [tex]A=\frac{2\pi}{3}\int^{\sqrt{7}}_{1}{x^{3}\sqrt{1+x^{4}}dy[/tex]
     
  5. Aug 3, 2009 #4
    Oh whoops, ok well having that in there, how could I continue this problem?


    EDIT: I see how this can be solved, substition method.

    Thank You.
     
    Last edited: Aug 3, 2009
  6. Aug 3, 2009 #5
    Do what Mark44 said to do.

    [tex]u=1+x^{4}[/tex]

    [tex]du=4x^{3}dx[/tex]
     
    Last edited: Aug 3, 2009
  7. Aug 3, 2009 #6

    Mark44

    Staff: Mentor

    Make that du = 4x3dx
     
  8. Aug 3, 2009 #7
    Haha oops.
     
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