Parametric Calculus: Surface Area Part 1

In this video I go over further into the wonderful world of calculus with parametric curves and this time go over part 1 of the proof for the formula for the surface area of a shape formed by rotating a curve about the x-axis. In part 1 I look at the case where the parametric equations can also be written as a typical function, y = F(x), which is the same as the surface area proof that I covered in my earlier video. In this case, we can simply use the substitution rule for definite integrals to change the basic surface area integral formula to one that accounts for the extra parametric parameter, just as in my earlier videos on arc length for parametric curves. Also just like for arc length, this formula derived using substitution is also valid even if the parametric equations can’t be written in the form of y = F(x) (i.e. a one-to-one function). I will illustrate this in part 2 by using polygonal approximation, again just like as for arc length, so stay tuned for that video!

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Related Videos:

Parametric Calculus: Arc Length Part 3 (Debunking My Own Video): https://youtu.be/udz4jzUgPBg Parametric Calculus: Arc Length Part 2: https://youtu.be/anD_j0nDDPA Parametric Calculus: Arc Length Part 1: https://youtu.be/AWvJDK-m6wQ Parametric Calculus: Areas: https://youtu.be/XdplYV61xlM Parametric Calculus: Tangents: https://youtu.be/deQwD2o0Sas Parametric Equations and Curves: https://youtu.be/Kd3XF4LZoFE Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg The Substitution Rule for Definite Integrals: http://youtu.be/AzmYfV1vsbU .

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