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Applications of Integrals: Surface Area
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In this video I go over the concept of determining the area of a surface of a general shape as we rotate it about an axis. The derivation is very similar to my earlier derivations of the length of a curve, and the volume of a shape formed as you rotate it about a curve. In this derivation, I use the length of a curve formula to first determine the length of a small section of a curve, and then rotate that curve about an axis to determine the surface area. Then I make the length very small and sum up to an infinite amount of small sections or bands which form the shape and thus we can write the surface area as an integral. This is a very extensive derivation video but it puts together many of the concepts of integrals and infinite sums so make sure to watch it!
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