- #1

Jovy

- 17

- 2

## Homework Statement

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis.

$$y=\frac 1 x$$

## Homework Equations

$$Volume=2\pi\int_a^b p(y)h(y)dy$$

## The Attempt at a Solution

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I see that there are two shells, therefore, I would do the integral twice. Meaning, ##Volume=2\pi\int_a^b p(y)h(y)dy+2\pi\int_a^b p(y)h(y)dy##

I'm having trouble identifying what h(x) are for both integrals. I know that you can change ##y=\frac 1 x## to be ##x=\frac 1 y## and I know that for both p(y)=y. I think the dashed lines indicates that ##y=\frac 1 2## is the axis in which it is being rotated.

How do you determine h(x)? Once I understand how to determine h(x) for both integrals, I know how to solve the rest of the problem.

this website has an image of the graph, incase the one I uploaded doesn't show:

**http://www.calcchat.com/book/Calculus-ETF-6e/7/3/17/**