MAT136H1 Lecture Notes - Strategy First

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

Document Summary

Question #3 (medium): finding volume by cylindrical shells. First, graph the region bound by the function and the lines. If the rotation is not typical or -axis, then measure from the line of rotation and modify the radius accordingly. If the height stretches vertically and the interval for integral moves across horizontally, the rotation is about the -axis. Similarly, if the height lies horizontally and the interval for integral moves up vertically, the rotation is about the -axis. Substitute the appropriately expressed height and the radius into the integral using cylindrical shells to calculate the volume: . Using cylindrical shells find the volume obtained by rotating the region bound by the curves about the given line. Factor the main function: to get the x intercepts at . Then the interval for integral is [ ]. Rotating the region about leaves the height for the cylindrical shells as .