Arc+length

Arc Length of Functions

This is an application of pythagoras combined with calculus. We know that math a^2+b^2=c^2 math So for the graph right we get that the distance along the curve is given by math s=\sqrt{(\Delta x)^2+(\Delta y)^2} math We can force out the x term as a common factor to get: math s=\sqrt{1+(\dfrac{\Delta y}{\Delta x})^2} \Delta x math So to find a length along a function between points a and b we can do this process an infinite number of times with infinitely small steps (with a definite integral) giving: math s= \displaystyle{ \int\limits_{a}^{b} \sqrt{1+(\dfrac{dy}{dx})^2} dx} math Note that the delta x is written as dx now we are dealing with very very small steps.