$6$:$321$

$6$

A solid is formed by revolving the region enclosed by the graphs of $y=(x-2{)}^2,x=2,$ and $y=4$ for $0x2$ about the given line. Sketch the region bounded by the graphs of the functions and the axis of revolution. Be sure to draw a representative washer or shell. Using the specified method, write an integral that gives the volume of the solid. Do NOT integrate.

$($a$)$ Revolved about the line given by $y=5.$

Washer Method:

Sketch of Region and Washer:

$R=q,$

$r=q,$

Integral that gives the volume of the solid:

$V=$

$($b$)$ Revolved about the line given by $x=-1.$

Shell Method:

Sketch of Region and Shell:

Shell Radius $=q,$

Shell Height $=q,$

Integral that gives the volume of the solid:

$V=$

Page $1$ of $2$

$2.$ Find the volume of the solid whose base is the region bounded by the curves $y=x^2+1,y=0,x=0,$ and $x=3$ and whose cross$-$sections taken perpendicular to the $x-$axis are squares.