Volume of Revolution

[ChaoticLlama]

The region bounded by \(\displaystyle y=sqrt{x}\), \(\displaystyle x=4\) and the x-axis is rotated about the line x=4. Find the volume of the solid using the a) Disk Method b) Shell Method.

I have two different answer from the two different methods. I have a feeling that the shell was done correctly, but I can't be sure.

Disk
\(\displaystyle \L\ V = \pi \int_0^2 {(y^2 )^2 } dy = \frac{{32\pi }}{5}\)

Shell
\(\displaystyle \L\ V = 2\pi \int_0^4 {(4 - x)\sqrt x } dx = \frac{{256\pi }}{{15}}\)

Thanks for any assistance.

 

[pka]

For your disk try: \(\displaystyle \L
\pi \int\limits_0^2 {\left( {4 - y^2 } \right)^2 dy}\)

 

[ChaoticLlama]

Thank you.