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Math Help - Surface Area of a Cycloid

  1. #1
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    Surface Area of a Cycloid

    Find the surface area generated by revolving one arch of the cycloid about the x-axis.

    Formula:
    2pi\int_{a}^{b}{y(t)}\sqrt{{x'(t)^2}+{y'(t)^2}} dt

    Thanks.
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  2. #2
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    Quote Originally Posted by jffyx View Post
    Find the surface area generated by revolving one arch of the cycloid about the x-axis.

    Formula:
    2pi\int_{a}^{b}{y(t)}\sqrt{{x'(t)^2}+{y'(t)^2}} dt

    Thanks.
    One arch is parametrised by 0 \leq t \leq 2 \pi.

    After doing the necessary differentiations, substituting and simplifying you get

    S = 2 \sqrt{2} \pi \int_0^{2 \pi} (1 - \cos t)^{3/2} \, dt.

    Your task now is to solve this integral.
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