Find the exact area of the surface obtained by rotating the given curves around the x-axis.
x = 3t - t^2, y = 3t^2, 0 <= t <= 1
My work:
2pi * Integral from 0 to 1 of 3t^2 root[ ( 3-2t)^2 + (6t)^2)] dt
2pi Int 0-->1 of 3t^2 root[ 40t^2 - 12t + 9]dt
This can't be right...