Volume

Area
The area bounded by a function, the line x=a, the line x=b (a<b), and the x-axis is equal to: math $\int_{a}^b {f(x)}dx math

The area between two functions is given by: math $\int_{a}^b {f(x)-g(x)}dx math where f(x) is the upper function, g(x) is the lower one, a is the first intersection, and b is the second (a<b).

If you end up with a negative answer, chances are, you flipped f and g.

__Disk Method__
Volume of a function bounded by f(x): Where f(x)=R, left endpoint=a, right endpoint=b: math \pi$\int_{a}^b {R^2}dx math

=__Washer Method__= Volume of a function bounded by f(x) on the outside and g(x) on the inside: Where f(x)=R, g(x)=r, left endpoint=a, right endpoint=b: math \pi$\int_{a}^b {((R)^2-(r)^2)}dx math

=__Shell Method__= Volume of a function rotated around the y axis, bounded by f(x) on top and g(x) below, found by taking the area of successive rectangular layers or "shells". Where left endpoint= a, right endpoint=b math 2\pi$\int_{a}^b {x*(f(x)-g(x))}dx math