# Homework Help: Surface Area

1. Apr 4, 2006

### G01

Find the surface area when this curve is revolved around the x ax

x = 1/3(y^2 + 2)^3/2 [1,2]

I set it up both ways and i get two really complicated integrals.

$$2 \pi/3 \int_1^2 \sqrt{\frac{y^2+y^4}{(y^2+2)^{2/3}}} dy$$

Yeah I cant figure out how to do this integral, and Im thinking there must be an easier way. The other way, integrating with x, seemed even more complicated If anyone can give me some hints, it'll be appreciated. Thanks.

2. Apr 4, 2006

### G01

sry i seem to be having trouble getting the latex to work. I'll try fix it, but im not to good at it so i cant promise anything.

3. Apr 5, 2006

Did you use the correct formula?

I tried part of the problem and it seems the final expression you needed to integrate is quite a simple one!

To find the surface area generated when a curve is rotated completely about the x-axis, you may use this formula...

$$2 \pi \int y \sqrt{1 + (\frac{dx}{dy})^2} dy$$

Please figure out the limits by yourself..

All the best!

4. Apr 5, 2006

thanks alot