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 $n = 1$:

Length for $n = 2$:

Length for $n = 4$:

(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 $\approx$