Thread: Surface Area of a Cycloid

1. Surface Area of a Cycloid

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

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

Thanks.

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

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

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

After doing the necessary differentiations, substituting and simplifying you get

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

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to find the surface area generated by cycloid

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