Refer to the figure and find the volume generated by rotatin

Refer to the figure and find the volume generated by rotating the given region about the specified line. R_2 about AB

R2 is bounded by line y=2 and bounded below by y = 2(x)^1/4

We are rotating about the line x =1 ( AB)

Since this is a vertical line, we will use cylindrical shell method
V = 2 b r * h dx

Each cylindrical shell has radius 1 -x

height of 2 - 2(x)^1/4

Volume = 2 b ( 1- x) * ( 2 - 2(x)^1/4)dx ; a = 0 ; b =1

V = 2(13/45)

= 26/45