Volume by Slicing


General Slicing Method

Suppose a solid object extends from x=a to x=b and the cross section of the solid perpendicular to the x axis has an area given by the function A that is an integrable function on [a,b]. The volume of the solid is:

Disk Method about the x-Axis

Let f be continuous with on the interval [a,b]. If the region R bounded by the graph of f, the x-axis, and the lines x=a and x=b is revolved around the x-axis, the volume of the resultin solid is

Washer Method

Let f and g be continuous functions with on [a,b]. Let R be the region bounded by y=f(x), y=g(x), and the lines x=a and x=b. When R is revolved about the x axis, the volume of the resulting solid of revolution is