Integral Calculus - surface area

Question

The given curve is rotated about the y-axis. Find the area of the resulting surface.

y=1/3x3/2,    5 ≤ x ≤ 21

It is rotated around the y axis so Ive been having trouble finding the area in terms of pi

Answer 1

The surface of just the curved part is given by the integral from 0 to 16

with integrand 2π(x+5)sqrt(1+(x^-3/4)). I won't even attempt to integrate that! Try Wolfram Alpha.

Then you have to add the surface of the 2 ends.