Arc Length Investigation
Move slider n, the number of subdivisions. The approximate length is shown in addition to the exact length using the arc length integral. Move sliders a, b, c, and d to change the function. Move points A and B to change the interval. Is the arc length approximation smaller or larger than the actual length? Is this true always, sometimes, never? Explain. Would there be a function or functions for which the approximation is longer? Explain why or why not.