Set up the definite integral for finding the indicated arc length. Then use the integration capabilities of a graphing utility to approximate the arc length.

A fleeing object leaves the origin and moves up the y-axis (see figure). At the same time, a pursuer leaves the point (1, 0) and always moves toward the fleeing object. The pursuer's speed is twice that of the fleeing object. The equation of the path is modeled by the following.
y = 1/3(x^3/2 − 3x^1/2 + 2)

How far has the fleeing object traveled when it is caught?

Question

Set up the definite integral for finding the indicated arc length. Then use the integration capabilities of a graphing utility to approximate the arc length.

A fleeing object leaves the origin and moves up the y-axis (see figure). At the same time, a pursuer leaves the point (1, 0) and always moves toward the fleeing object. The pursuer's speed is twice that of the fleeing object. The equation of the path is modeled by the following.
y = 1/3(x^3/2 − 3x^1/2 + 2)

 
How far has the fleeing object traveled when it is caught?