||Computing Signed Areas and Volumes with Maple
||Shengxiang XIA, Wei-Chi YANG and Vladimir SHELOMOVSKII
The signed area bounded by a parametric curve with respect to a slanted line and the signed volume bounded by a smooth parametric surface, a plane and the perpendicular projection from the surface to the plane were discussed in . In this note, in addition to the integration method described in , we introduce a transformation method to further discuss how to find the volume of the solid bounded by an orientable smooth surface, especially for a real closed quadric surface and a plane. We present Maple procedures based on integration and transformation methods used to evaluate signed areas and volumes. The procedures are designed with formal parameters which can be easily used or modified by instructors and students.