Hello,
I perfectly understand both methods (discs and shells) my only problem is to know which one to use.
Let's say I had a problem it would be hard fo me to know which method to use... and would both work each time?
Thank you
It's more a matter of convenience. There's not a function I can think of that you couldn't weasle through with either method. A torus is a common example where shells are a little more stright forward. This is a good example where washer would be preferred.
Usually one method has easier integrations and/or one integral opposed to two integrals. Case in point revolve the region bound by
$\displaystyle y = x, y = 2-x, y = 0 $ about the $\displaystyle y$ -axis
Shells: $\displaystyle 2 \pi \int_0^1 x\cdot x\,dx + 2 \pi \int_1^2 x(2-x)\,dx$
Washers $\displaystyle \pi \int_0^1 (2-y)^2-y^2\, dy$