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Lecture

6.3 Volumes by Cylindrical Shells Question #4 (Medium)

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Department
Mathematics
Course
MAT136H1
Professor
All Professors
Semester
Winter

Description
6.3 Integral Applications Cylindrical Shells Question #4 (Medium): Volume Estimation by Cylindrical Shells Using the Midpoint Rule Strategy Using the cylindrical shells, volume estimation is: ∑ ̅ ̅ , where ̅ is the midpoint of the -th subinterval[ ]. Given the number of rectangles, the entire interval is divided with a midpoint for each subinterval. Using the midpoints, the radius and height of each cylindrical shell is computed based on the given function. Summing all over the subintervals gives the volume estimation. Sample Problem Estimate the volume using cylindrical shells based on the Midpoint Rule, where and the bound region is rotated about the given line. ( ), , about Solution Since and the whole interval is ], then . So the whole interval is split into ] [ ] [ ] [ ] [ ] M
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