In this video I go over another example on using the arc length formula to determine the length of the curve and this time show that it is sometimes easier to deal with x as a function of y, i.e. x = f(y), instead of the typical y = f(x) that we are accustomed to. This is especially the case in this example in which I solve for the length of the curve y^2 = x from the points (0, 0) to (1, 1). Since we are given the function already in terms of x = f(y) it is easier working with this function as opposed to dealing with a square root as in y = +/- sqr(x). When dealing with the function this way, we can still use the arc length formula, but we just have to simply switch the variables.
This is a very useful example because it illustrates how sometimes it is easier to deal with x as a function of y, as well as showing how the square root that appears in the arc length formula usually leads to very difficult or even impossible integrals to explicitly evaluate, as I will show in my next video.
Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!103189&authkey=!ADrDTOz4ca15ggI&ithint=file%2cpdf
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-arc-length-example-2-x-f-y
Related Videos:
Applications of Integrals: Arc Length: Example 1:
Applications of Integrals: Arc Length Proof:
Simple Proof of the Pythagorean Theorem:
Trigonometric Integrals: Example 8: sec(x)^3:
Trigonometry Identities: Proof that sin^2(x) + cos^2(x) = 1: .
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I don't always determine the arc length of a curve but when I do I usually deal with x as a function of y ;)
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-arc-length-example-2-x-f-y