In this video I go over further into Calculus with Parametric Curves and this time look at calculating the area underneath a parametric curve. The area underneath a curve y = F(x) can be calculated by using definite integrals. But for parametric equations x = f(t) and y = g(t), I show that we can use the Substitution Rule for Definite integrals to replace the x term with the parameter t. But when we do this it is important to ensure that the interval of the parameter is such that the curve is traced just once, otherwise we will obtain a larger area. This is a very useful video on using the substitution rule to re-arrange definite integrals to account for parametric equations, and which I will be using in later videos, so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhuM2xu-1hUBChBGPzQ
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/parametric-calculus-areas
Related Videos:
Parametric Calculus: Tangents:
Parametric Equations and Curves:
Integrals and Areas Between Curves:
The Substitution Rule for Definite Integrals: .
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I don't always calculate the area of a parametric curve but when I do I usually use the Substitution Rule for Definite Integrals ;)
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/parametric-calculus-areas
Calculus!!. This takes me way back to High School, and Yes I loved calculus- differentiating and integrating multiple functions. I'm kinda rusty now since my major is Biology. Good video tho. Keep it up.
The calculus of mathematics
Really very special article