In this video I go over further into Calculus with Parametric Curves and this time derive the formula for the Arc Length, which is the length of a curve. I go over Part 1 of the arc length derivation, which looks at the specific case in which the parametric equations x = f(t) and y = g(t) can be written in the standard form y = F(x). In the derivation I use the Substitution Rule for integrals to convert the standard formula for arc length, which I have covered in my earlier videos. In the next part I show that this formula for arc length is still valid even if the curve can’t be written as y = F(x). But to do that I use polygonal approximation, which is quite amazing so stay tuned for the next video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhuQKA0sSyNWcgDiLhg
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/parametric-calculus-arc-length-part-1
Related Videos:
Parametric Calculus: Areas:
Parametric Calculus: Tangents:
Parametric Equations and Curves:
Integrals and Areas Between Curves: The Substitution Rule for Definite Integrals: http://youtu.be/AzmYfV1vsbU
Applications of Integrals: Arc Length Proof: .
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I don't always find the length of a parametric curve but when I do I usually prove the similar case first ;)
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/parametric-calculus-arc-length-part-1