1. ## Cylindrical Shell Method

I need help asap. Finals in couple hours.

f(x) = SquareRoot(x^2 + 9) over [0,3]

I got 2pi integral from 0,3 and inside of integral i put x(SquareRoot(x^2 + 9)dx.

I know that I'm suppose to multiply it out but I dont know how to im suppose to multiply that because of the square root. help would be appreciated.

Sorry for not using the symbolic characters.

2. You didn't say which axis you have to revolve it around. y axis?.

3. yes, sorry. the y-axis.

4. In that event, you set up is correct.

$2{\pi}\int_{0}^{3}x\sqrt{x^{2}+9}dx$

Now, let $u=x^{2}+9, \;\ du=2xdx, \;\ \frac{1}{2}du=xdx$

Don't forget to change your limits of integration:

$(3)^{2}+9=18, \;\ (0)^{2}+9=9$

So, your new limits are 9 to 18 and you have:

${\pi}\int\sqrt{u}du$