Homework Help: Basic Integral calculus volume problem

1. Nov 7, 2007

Hi everyone, this is my first time posting on these forums. If I am doing anything wrong, please let me know.

I am having a lot of trouble with conceptualizing rotating lines around the X- and Y-axis.

The problem I am trying to visualize right now is...

Using integrals to represent the volume of the solid formed by...

Y = sqrt(x)+3, Y = 7 - (1/2)x, and the Y-axis. Rotated around the line Y = 3.

my gut feeling for this problem is...

To setup the integral so that it looks like this...

setting the two equations equal, and differentiating for X, the integral is from [0,4]

and this is then my integral setup.

(Pi(7 - (1/2)x - 3)^2 - Pi(sqrt(x) + 3 - 3)^2)DX

This creates a washer with outer radius of Pi(4 - 1/2x)^2 and inner radius Pi(x)

I am pretty new to calculus, and I understand this is a very basic concept.
I am just looking for some pointers on how to approach these kinds of problems.

and is this even a correct way to solve this problem?

2. Nov 7, 2007

Dick

If you are new to this stuff, then you are way ahead of the curve. That looks good to me.