Arc+Length+(BC)

Suppose you were asked to find the length of the arc of a function on a set integral similar to the graph below.



A very simple method of doing this would be to place a string along the function and then straighten out along the x-axis to find the distance. This has a wide range for human error so mathematicians often look to another method.

To start, someone may draw various points along the function and connect them with multiple straight lines, then find the distances of those lines using the Pythagorean Theorem. This equation can be seen as:



To make these estimates even more accurate, the dots would be placed even closer together to create more straight lines. As the change in x and the change in y get closer and closer together, they can be rewritten in the equation as dx and dy:



All of the distances put together would give you the equation:

OR OR

This equation can be seen as fairly useless to a mathematician until it is rewritten as: (y' = dy/dx)



Here are some sample questions from: http://www.cliffsnotes.com/study_guide/Arc-Length.topicArticleId-39909,articleId-39908.html.


 * 1)** Find the arc length of the graph of [[image:http://media.wiley.com/Lux/40/39840.ngr001.gif align="absmiddle"]] on the interval [0,5].


 * 2)** Find the arc length of the graph of //f(x//) = ln (sin //x//) on the interval [π/4, π/2].

Answers:

1)

2)