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## Homework Statement

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 5. (Use disk method)

$$ xy = 3, y = 1, y = 4, x = 5 $$

## Homework Equations

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The formula using for disk method is of the form:

$$ \pi \int (r(x/y))^2*(dx/y) $$

## The Attempt at a Solution

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So first I graphed this out, and came up with a region, like so (represented by the white region):

In disk method, when rotating around a vertical axis, the differential of dy is used.

Setting this integral up, our limits are y = 1, to y = 4, as given in the problem statement.

My main question is how do we represent the r in the disk method equation, when the axis is meant to be around x = 5, and not the y-axis.

The best I could think of would be:

$$ \pi \int_{1}^{4} (\frac {y} {3} + 5)^{2} dy $$

However, something tells me this isn't the right approach, because I'm not seeing the logic behind whether or not I should add, subtract, or subtract from the x = 5.

Thank you.