Arc Length of a Space Curve

Given a space curve one can find the arc length between two "times" by finding the integral of the magnitude of the derivative of the space curve across those two times. Wow... ok... that was a lot, lets see what the formula looks like:

Where:

• is the distance along the curve
• is "time" or any other input variable
• is the starting "time" (think ) and is the ending time
• is derivative of the space curve

See Multivariable Calculus Notes - Chapter 13 - Sections 3-4 for notes and more information.