Arc length of functions in one variable

The  exercise appears under the Integral calculus Math Mission. This exercise finds arc length of various functions in Cartesian coordinates.

Types of Problems
There are two types of problems in this exercise:


 * 1) Find the expression for the arc length: This problem has a function an interval along which it wants the arc length. The student is asked to select the expression from a multiple choice list that correctly expresses the arc length.Alofiov1.png
 * 2) Find the value of the arc length: This problem has a function and an interval. The student is asked to find the arc length along the function over the interval.Alofiov2.png

Strategies
Knowledge of the Pythagorean theorem and integration techniques are encouraged to ensure success on this exercise.
 * 1) The arc length in one variable is given by the integral of \sqrt{1+(dy/dx)^2}.
 * 2) The arc length is motivated by the Pythagorean Theorem with side lengths of dx and dy.
 * 3) The integrand on these problems is often complicated, making it difficult to get exact answers unless the problem is written very carefully.

Real-life Applications

 * 1) Like many other concepts in calculus, limits can now be used to approximate curvy objects by straight lines to find length, so there are applications to any situation where one wishes to find the length around non-regular objects (such as shorelines).