2

1

For a parabola with :

Arc length can be calculated by solving :

By integrating and solving this, we get:

Using this formulla and we can find arc length for the parabola you asked for:

by subsituting

a = b

h = a

We get:

Integration ( b^{2} + 4 * a )^{1/2} + b^{2}/2*a sinh^{-1}(2 * a/b)

1

The length of parabolic arc from 'a' to 'b' is calculated using integration of √( 1+[f ′(x)]^{2 }) from a to b.

[ f ′(x) = derivative of f(x) ]

L = ∫ √( 1+[f ′(x) ]^{2 })dx

Integrate from a to b. ( In your case '-b' to 'b' )