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^{2}and y = x + 2.

(a) Sketch the region R and label the points of intersection between the two curves.

(b) Suppose we rotate R about the x-axis. Compute the volume of the resulting solid.

(c) What is the volume of the solid obtained by rotating the region R about the line x = 2?

## Homework Equations

We need to know the equation for solving volume using a definite integral with the disc method and cylindrical method.

## The Attempt at a Solution

I have part (a). For part (b), I set up the problem using the disc method which is the definite integral from [-1,2] of A(x) dx.

The set up looked like The definite integral from [-1,2] of pi(x+2)

^{2}dx.

After solving this, I got 21pi but am doubtful of my answer.

For part (c), I set up the problem using the cylindrical method which is the definite integral from [-1,2] of 2*pi*x (x+2)dx with radius x, circumference 2pi x and height x + 2. I got 12pi but am once again doubtful of my answer.

Am I on the right track? Help please?