Consider the Region R Bounded By $y = \frac { 1 } { 2 } \sqrt { x } , y = 1$

Essay

Consider the region R bounded by $y = \frac { 1 } { 2 } \sqrt { x } , y = 1$ , and the y-axis.(a) Find the area of R.(b) Find the average height of R.(c) Find the volume, V, of the solid obtained by rotating R about the x-axis.(d) A cross section of the solid generated by part (c) taken perpendicular to the x-axis is a washer. Determine the average area of the cross sections of the solid.