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Surface area of a revolution

  1. Mar 5, 2007 #1
    (my first dealings with latex.. so bare with me if this looks a little messed up at first :rolleyes: )
    1. The problem statement, all variables and given/known data
    Find the surface area for the equation:
    [tex]x = 3y^{4/3} - \frac{3}{32}y^{2/3}[/tex]

    with bounds [tex]-216 \leq y \leq 216[/tex]

    rotated about the Y-axis.

    2. Relevant equations

    [tex]\int^a_b 2\pi f(y) \sqrt{1+(\frac{dx}{dy})^2}[/tex]

    3. The attempt at a solution

    well... going with that equation i get to this point:

    [tex]2\pi \int^{216}_{-216} (3y^{4/3} - \frac{3}{32}y^{2/3})(4y^{1/3} + \frac{1}{16}y^{-1/3}) [/tex]

    from there I tried to multiply out the equation and solve the integral with the bounds, but it isn't giving me the correct answer. I'm not sure what I'm doing wrong. I suspect I have to break the integral up smaller pieces but im not sure where to break it at.
    Last edited: Mar 5, 2007
  2. jcsd
  3. Mar 5, 2007 #2
    you have substituted dx/dy incorrectly into the equation

    dx/dy should be inside the root
  4. Mar 5, 2007 #3


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    Because of the symmetry, you can integrate from 0 to 216 and then multiply by 2. What do you get?
  5. Mar 5, 2007 #4
    ok... when I multiply out the integrand I get:

    [tex]2\pi [12y^{5/3} - \frac{3}{16}y^2 - \frac{9}{2048}y^{1/3}]^{216}_{0}[/tex]

    when I evaluate at 216 & 0, i get 7552892.305... I multiply that by 2 (symmetry) and then multiply that by 2pi, which gives me 94925010.28

    edit... nevermind, i made a stupid math mistake. Got it right now, thanks a ton HallsofIvy!
    Last edited: Mar 5, 2007
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