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Here is the question:

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified x-axis.

Here are the parameters:

$$y = 4x - x^2, y = 3\text {; about }x = 1$$

So here are my choices for radius and height:

radius = $x - 1$

height = $4x - x^2 - 3$

So...is this setup right?

$$ \int_1^3 2 \pi (x - 1) ( 4x - x^2 - 3)\, dx$$

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  • $\begingroup$ looks good to me! $\endgroup$ – imranfat Apr 19 '18 at 16:14
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You are correct.

The volume of revolution is presented by $$\int_1^3 2 \pi (x - 1) ( 4x - x^2 - 3)\, dx$$

and you have explained it well in detail.

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  • $\begingroup$ Ok cool... my main concern was my calculation of radius and height. $\endgroup$ – Jwan622 Apr 19 '18 at 17:19

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