Homework SourseUse the method of cylindrical shells to find the volume of t
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by x=1+(y-2)^2, x=2 about the x-axis. Sketch the region and a typical shell.
Solution
volume of the solid
V = integral of 2y(1+(y-2)2)dy from 0 to 2
= integral of 2(y+y3+4y-4y2)dy from 0 to 2
= 2(5y2/2 + y4/4 - 4 y3/3) from 0 to 2
