...don't you mean:Fermat said:The shell Method:
When taking a volume of revolution about the y-axis, the formula is,
[tex]V = \int_{x_0} ^{x_1} xy \ dx[/tex]
where x is the radius of the shell, dx represents the shell thickness and y is the length, or height, of the shell.
Since, in this case, you are taking negative y-values, then you will get a negative answer for the volume. Simply change the sign.
You have two curves to contend with, so you should make up the integral like this,
[tex]V = \int_0 ^1 xy_1 \ dx + \int_1 ^2 xy_2 \ dx[/tex]
[tex]\mbox{where}\ y_1\ \mbox{is}\ \sqrt{x}\ \mbox{and}\ y_2\ \mbox{is}\ (x-2).[/tex]
yes,apmcavoy said:...don't you mean:
[tex]V=\mathbf{2\pi}\int_{a}^{b}xf(x)dx[/tex]
Sorry about the confusion there. I'm afraid I misread your work. Actually, I'd never heard of the shell method before.denian said:thank you, but im a bit confused.
im doing some self-study here, and the formula they wrote in the book is what i wrote in the first line.
btw, the x-axis is the axis of rotation.
nvm. i try to figure it out again :)