(a) Graph the curve y = x 3(4-x), 0 ¤ x ¤ 4. (b) Compute the lengths...

Question:

(a) Graph the curve y = x 3ˆš(4-x), 0 ‰¤ x ‰¤ 4.
(b) Compute the lengths of inscribed polygons with n = 1,2 and 4 sides. (Divide the interval into equal subintervals.) Illustrate by sketching these polygons (as in Figure 6).

(c) Set up an integral for the length of the curve.
(d) Use your calculator to find the length of the curve to four decimal places. Compare with the approximations in part (b).