Consider the curve
y = x \sqrt[3]{4-x},\quad 0 \le x \le 4.
(a)
Divide [0,4] up into 1, 2, and 4 equal segments, and draw line segments between
those values on the graph. Then compute the length of the polygonal curve you drew.

Length for

Length for

Length for

(b) Set up an integral for the length of the curve, and then use a calculator or a computer algebra system to find the length of the curve to four decimal places.

Length of curve

You can earn partial credit on this problem.