find the volume of the solid obtained by revolving the region bounded by the graphs of y=2+4x-x^2 and y=2 about the line y=2.

Answer 1

y-2=4x-x^2
The volume=pi*Int.[0,4](4x-x^2)^2dx=
pi*Int.[0,4](16x^2-8x^3+x^4)dx=
pi*(16/3x^3-2x^4+1/5x^5)[0,4]=
pi*(1024/3-512+1024/5)=pi*1024/30