6.2 Integral Applications
Question #1 (Easy): Finding the Volume of a Solid Rotated About a Horizontal Line
To find the volume of a solid, first the area expression for the base needs to be established:
( ) .
When the solid is obtained from the area bound by two functions, he shape of the cross-sectional area is
called a washer. Once the expression of the area of the base for the cross-sectional cylinder is
established, the integral is set over the interval , which is either given by the question or needs to
be algebraically determined from the points of intersection. When these information are determined,
the volume can be calculated as: ( ) .
Find the volume of the solid that is obtained by rotating the area bound by two functions about the
given line. Include the sketch of the bound area, as well as the solid and a typical sample disk or washer.
√ , , abou