# Worksheet15-1.pdf - MATH 140 WORKSHEET#15 1-5.2 Volumes I...

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MATH 140 WORKSHEET #15 - 1 -5.2 VolumesI. Volumes by Disks In order to find the area of the region Renclosed by the curve  xfyand the x-axis for bxaneed to cut the region into n approximating rectangles with areas Aiand evaluate  baniindxxfA1lim. If the region Ris rotated about the x-axis, a solid with cylindrical symmetry is obtained (a solid of revolution). In the process, each one of the approximating rectangles generates a disk whose radius is the height of the rectangle and whose thickness is the width of the rectangle. In other words, the solid of revolution can be thought of as being sliced perpendicularly to its axis of rotation into a large number of thin disks. What expression gives the volume of a disk?niinVV1limxy xfyRabxyiixfyxixrtxy xfyxxy, we How can we express the volume Vof the solid of revolution in terms of the volumes Viof the approximating disks? niinVV1limxy xfyRabxyiixfyxixrtxy xfyxxy
MATH 140 WORKSHEET #15 - 2 -