1. The problem statement, all variables and given/known data

Hello!

English is not my native language so I hope the terminology is right.

Q:
Find the volume generated by the curve y=1/x+2, positive x- and y-axis and the line x=1.
Calculate the volume obtained by rotation around the:
a) x-axis
b) y-axis

2. Relevant equations
The text book use this one:
[tex]Vx= \pi \int_{a}^{b}(f(x))^{2} dx[/tex]

3. The attempt at a solution
a) I got this one right:

I would have to say that the shell method would be easier here,
2*∏*∫(SHELL RADIUS)*(SHELL HEIGHT) dx
Of course the limits of integration would be [0,1]

Thanks,
I have never seen this methods. The text book & teacher only use pi(f(x))² and Washer method. Should it not be possiable with disc/washer?

With [0,1] I got:
[tex]Vy = 4\pi ((1-\frac{1}{4*1}-ln1) - (\frac{0}{0}-\frac{1}{4*0}-ln\frac{0}{0})) = 4\pi (1-\frac{1}{4}) = 4\pi (3/4) [/tex]
Isn't the parentheses with 0 undefined, so I can't really use lower limit 0?

Using the shell method I got the same answer as Zondrina, but using your integral Hacca, I evaluated the integral on my own, and on wolfram, and both came to the same conclusion of 0.0448.