# Shell method

1. Mar 26, 2008

### DaOneEnOnly

1. The problem statement, all variables and given/known data
Find the volume of the solid of revolution:
F(x)=2x+3 on [0,1]
Revolved over the line x=3 and y=5

2. Relevant equations
Shell Method: 2$$\pi$$$$\int$$$$^{b}$$$$_{a}$$x[f(x)-g(x)]dx
obviously just sub y for dy
Disk Method: $$/pi$$$$/int$$$$^{b}$$$$_{a}$$[F(x)$$^{2}$$-G(x)$$^{2}$$dx

3. The attempt at a solution
line x=3: 2$$/pi$$$$/int$$(3-x)(2x+3)dx =115.19

answer key is unfortunately in disk method which I don't like as much:
$$/pi$$$$/int$$$$^{3}$$$$_{0}$$(9-4)dy + $$/pi$$$$/int$$$$^{5}$$$$_{3}$$(3-((y-3)/2))$$^{2}$$-4dy

=78.91

line y=5: 2$$/pi$$[tex/int[/tex]$$^{5}$$$$_{0}$$(5-y)(1-((y-3)/2)) =130.8996

answer key/ disk method: $$/pi$$$$/int$$$$^{1}$$$$_{0}$$(25-(5-(2x+3))$$^{2}$$dx

=77.206