Parametric Calculus: Areas: Example 1: Cycloid

In this video I show how we can use parametric calculus to determine the area of an arch of a cycloid. The first step is to write the integral using the parameter, by following the steps outlined in my earlier video on area. The area of an arch of the cycloid turns out to be 3πr^2 which is 3 times the area of the circle that forms the cycloid. Galileo first guessed this result but it was the mathematicians Gilles de Roberval and Evangelista Torricelli that later proved this. Their proofs were more complicated because they did not have access to the more advanced forms of calculus which I have outlined in this video. I go over a brief yet very interesting history lesson on these mathematicians and the determination of the area of a cycloid, so make sure to watch this video until the end!

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Related Videos:

Parametric Calculus: Areas: https://youtu.be/XdplYV61xlM Parametric Calculus: Tangents: https://youtu.be/deQwD2o0Sas Parametric Equations and Curves: https://youtu.be/Kd3XF4LZoFE Integrals and Areas Between Curves: http://youtu.be/2F03KMLIzbk The Substitution Rule for Definite Integrals: http://youtu.be/AzmYfV1vsbU .

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