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Multi Calc, Lec 3B: Surface Area of Solid of Revolution (from Parametric Curve)

For a parametric curve (x,y)=(f(t),g(t)), we use infinitesimal elements (a.k.a. "differentials" or "elements" or "increments") to derive the formula for the surface area of a solid of revolution obtained by rotating the parametric curve around the x-axis. The arc length element ds is used to find the area element dA in terms of the time element dt. Infinite Powers, How Calculus Reveals the Secrets of the Universe: https://amzn.to/37PBMjb. Multivariable Calculus, Lecture 3B #MultivariableCalculus #SurfaceAreaOfSolids #SolidOfRevolution #infinitesimals #differentials Links and resources =============================== 🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinn... 🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/ 🔴 Follow me on Twitter:   / billkinneymath   🔴 Follow me on Instagram:   / billkinneymath   🔴 You can support me by buying "Infinite Powers, How Calculus Reveals the Secrets of the Universe", by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA. 🔴 Check out my artist son Tyler Kinney's website: https://www.tylertkinney.co/ 🔴 Desiring God website: https://www.desiringgod.org/ (0:00) Surface area of solid of revolution (parametric equation version) (4:27) Arc length element ds (an "infinitesimal" or "differential") (10:01) Surface area element dA (in terms of ds and then in terms of dt) (12:07) Surface area integral AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.