Area Between Two Curves. Math 5A. The Problem. Find the volume of the solid formed when the region bounded by y=sqrt(x) , x=4 and the x axis is revolved about the x axis. The Idea Behind the Solution. Suppose we tried slicing this solid into 4 pieces by slicing perpendicular to the x axis.
Area Between Two Curves
Suppose we tried slicing this solid into 4 pieces by slicing perpendicular to the x axis.
Those four slices would look approximately like the four circular disks shown at the right, only the outer surface would not be as straight. We can approximate the volume of the solid by computing the volume of these four disks.
The volume of each disk is pr2h where h is the thickness of each disk
(1 in this case, in general) and r is the functional value at a a point in the subinterval.
Approximation using 4 disks. For a better approximation, use more disks.
For a solid formed by revolving a region bounded above by f(x) on [a,b] about the x axis…