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Calculus of parametric equations (finding surface area)

  1. Sep 21, 2005 #1
    I was wondering what the surface area would be when the curve:

    x=e^tsint,
    and y=e^tcost where (t) is greater than or equal to (0) and (t) is less
    or equal to pi divided by (2).
    when it is revolved about
    a) the x-axis
    b) the y-axis (approximation with calc. (how?))
     
  2. jcsd
  3. Sep 21, 2005 #2
    Around the x-axis you have:

    [tex]\text{SA}_x=2\pi\int_{a}^{b}f(x)\left(\sqrt{1+f'(x)^2}\right)dx[/tex]

    ...the y-axis you have:

    [tex]\text{SA}_y=2\pi\int_{a}^{b}x\left(\sqrt{1+f'(x)^2}\right)dx[/tex]

    And I assume you can figure out what f(x) and dx are in terms of your parametric equations...
     
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