MAT136H1 Lecture : 6.2 Volumes Question #2 (Easy)
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Question #2 (medium): finding the volume of a solid rotated about a vertical line. When the area is rotated about a vertical line, the extends horizontally, then naturally the of the disks will rise vertically, yielding or . Therefore, integration is done with respect to and all functions in the integral are written in terms of . If the functions are initially written in terms of. , they must be rearranged to be re-written in terms of . , where the is expressed in terms of . Whether integrate over or , the area of the cross-sectional disk is still evaluated as: The interval [ ] is the start and ending point along the -axis. Find the volume of the solid that is obtained by rotating the area bound by the functions about the given line. Include the sketch of the bound area, as well as the solid and a typical sample disk or washer.
