Hello, sgares!
Your algebra is off . . .
Your set-up is correct . . .Use the method of cylindrical shells to find the volume of the solid obtained
by rotating the region bounded by about the y-axis.
But this is: .
. . . Try it now . . .
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by y = 6sqrt(x) and y = 6x^2 about the y axis.
I keep getting ~9.425 which is wrong, but I'm not sure why yet!
Here is how I come to my answer time and time again...
S = integral sign loL
V = S 2pi(x(6sqrt(x) - 6x^2))
V = 2pi S (6x - 6x^3)
V = 2pi [3x^2 - (3/2)x^4] from 0-1
V = 9.4248