MAT136H1 Lecture Notes - Riemann Sum

• School: UTSG
• Department: Mathematics
• Course: MAT136H1
• Professor: all

Document Summary

Question #4 (medium): volume estimation by cylindrical shells using the midpoint rule. Using the cylindrical shells, volume estimation is: 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. Estimate the volume using cylindrical shells based on the midpoint rule, where and the bound region is rotated about the given line. Since and the whole interval is [ ], then. So the whole interval is split into [ ] [ ] [ ] [ ] [ ] Midpoint for each subinterval is then , where. Plug in the information to the sum expression: Therefore using cylindrical shells based on the midpoint rule, the volume estimation of the region bound by (