# Integral word problem. Did I set this up correctly?

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?

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

• looks good to me! – imranfat Apr 19 '18 at 16:14

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