Arc length formula

The arc length formula which is explained on this page, is used in calculus to find the length of a graph on a given domain.
This page contains an explanation about it and provides some exercises in order to get familiar with the formula.
The formula for calculating the arc length is as follows:
In some cases, you might want to use integration by substitution to solve the integral.
*α* (degrees) and radius *r* can be calculated with this formula:

Circle

The length of a circle segment with angle Exercises

- Given is a circle segment starting at -10°, ending at -25° and diameter 3. Calculate the length of the arc.
- What is the length of the the line y = 35x, given that 2 ≤ x ≤ 10?
- Calculate the length of the line y = 5x
^{3/2}starting at x = 0 and ending in x = 3.

Solutions

- 2π · (15/360) · 1.5 ≈ 0.393