# Shell method

1. Homework Statement
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. Homework 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

## Answers and Replies

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The last part since I wasn't allowed so many $$1. Homework Statement Find the volume of the solid of revolution: F(x)=2x+3 on [0,1] Revolved over the line x=3 and y=5 2. Homework Equations Shell Method: 2[tex]\pi$$$$\int$$$$^{b}$$$$_{a}$$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$$\pi$$$$\int$$$$^{5}$$$$_{0}$$(5-y)(1-((y-3)/2)) =130.8996

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

=77.206

The last part since I wasn't allowed so many $$3. The Attempt at a Solution line x=3: 2[tex]/pi$$$$/int$$(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$$\pi$$$$\int$$$$^{5}$$$$_{0}$$(5-y)(1-((y-3)/2)) =130.8996

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

=77.206

the first number in the integral is the upper bound and the second is the lower.... I just can't get it to be formatted the right way for some reason.

EDIT: sry about the repeat... said database error so I thought it didn't go through.

EDIT: OMG there's 2 double posts.... srry

Last edited:
HallsofIvy
Homework Helper
1. Homework Statement
Find the volume of the solid of revolution:
F(x)=2x+3 on [0,1]
Revolved over the line x=3 and y=5
Is this two separate problems? It doesn't appear to be from your work but what do you mean by "revolved over" two separate lines? In any case, "F(x)= 2x+3 on [0,1]" doesn't define a region. Do you mean the region bounded by y=2x+ 3, y= 0, x= 0, and x= 1?

2. Homework 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$$\pi$$$$\int$$$$^{5}$$$$_{0}$$(5-y)(1-((y-3)/2)) =130.8996

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

=77.206