Hello. First, I would like to say that this is my first post so thank you in advance for any help. I have tried numerous ways of setting this problem up and I have not been able to come up with the correct answer. Also, I'll try to figure out how to post with all the correct symbols, but for now I will just do the best I can with what my keyboard has on it.

The problem tells me to use the Shell Method to find the volume of the solid generated by revolving the region about the given axis.

The region bounded by y=5x^(1/2) , y=5 , and x=0 , about the line x=1.

Here is one of the ways I have tried setting this up.

Integral symbol = $

After finding 5x^(1/2)=5 = x=1 I Integrate on the x-axis from 0-1

$2pi[shell radius][shell height]dx

=2pi$[1-x][5x^(1/2)]dx

I come up with 8pi/3 but the answer sheet says I am supposed to get 7pi/3.

I applogize again for the shabby way my post looks. I'm a little embarrassed after looking at some other peoples questions.