Determine the distance along the x-axis that the arc length of the parabola traverses, for example, the length of a parabola between x = 0 and x = 1. These two endpoints act as limits for the measurement.
Write down the parabolic arc length equation twice with the second being subtracted from the first. For reference, the parabolic arc length equation is 1 / 4 [ 2x + √(1 + 4x^2) + Ln (2x + √(1 + 4x^2))].
Substitute the end of measurement values into each equation. The larger endpoint is substituted into the first equation, and the smaller endpoint is substituted into the second equation.
Perform the indicated operations and subtract the final value of the second equation from the first. The resulting value is the arc length of a parabola between the limits specified.