# Integration help

1. Nov 11, 2008

### elitespart

The loop 9y^2=x(3-x)^2 is revolved about the y-axis. Find the area of the surface generated this way.

I just need help with integration:

$$4\pi\int x\sqrt{\frac{x^{2}+2x+1}{4x}}$$

I know I can pull out the 4 but after that I'm lost. Any suggestions?

2. Nov 11, 2008

### Dick

x^2+2*x+1=(x+1)^2. There's another thing you can pull out.

3. Nov 11, 2008

### elitespart

oh sweet. Thanks. oh if anyone has time to check could you please let me know if I set up the integral properly?

4. Nov 11, 2008

### Dick

You know there is something special about problems like surface area and arc length? With that square root in them, you can almost never do them exactly. You have to set up a problem carefully to get it to have an exact solution. Since yours cracked so easily, I'm going to guess it's correct, just based on probability. But, sure, I'll check it.

5. Nov 11, 2008

### elitespart

thanks. and I forgot to add that it's from 0 to 3. and you're right - I ended up with 60.9422...

Last edited: Nov 11, 2008
6. Nov 11, 2008

### Dick

It looks pretty good as far as the integral goes. Why do you have 4pi instead of 2pi. I might just be getting tired.

7. Nov 11, 2008

### elitespart

Because I'm only considering the top half of the loop in the integral.

8. Nov 11, 2008

### Dick

Oh. So there's negative y's as well. I was getting tired. Carry on.

9. Nov 11, 2008

### elitespart

lol no worries. Thank you again.