[Blindmath] volume of rotational solids (calculus)

[Alex Hall]

Hi all,
This is not a request for help in finding this sort of thing. Rather,
I am wondering if it can be done purely algebraically so I do not have
to try to imagine the graph. Example:

Find the volume of the solid formed by rotating the function y=x^2
around the x-axis from x=0 to x=4.

This one is a pretty simple example, and should be pi*x^5/5, I think.
This is using the Disk Method, but what happens with the Washer method
or the Shell method, where you might have space in the solid where the
function is not defined? Currently, I have to try to imagine the graph
to "see" the radius to use, any undefined portions, and so on. What I
am wondering is if anyone has dealt with this and has found any way to
do it all with algebra or some other non-graphical method. If so,
please share! Thanks.

-- 
Have a great day,
Alex (msg sent from GMail website)
mehgcap at gmail.com; http://www.facebook.com/mehgcap