MTH 162 Midterm: MTH 162 University of Rochester Exam1Fall 07

• School: University of Rochester
• Department: Mathematics
• Course: MTH 162
• Professor: All

Document Summary

Sketch s, along with a typical cross-section of s, and nd the volume of s using the washer method (also called the cross-sectional method. ) Solution: (a) the area of the region is. 2 (b) using washers, the volume is. 10: (13 points) again consider the curves described by y = x2 and y = x. (a) let s be the solid obtained by rotating the region bounded by these curves about the y-axis. Sketch s and nd the volume of s using whichever method you want (washer method or cylindrical shells. ) Solution: (a) using cylindrical shells, the volume of the solid is: (2 x)( x x2) dx = 2 z 1. Math 162 (calculus iia) (b) using cylindrical shells, the radius is 4 x and the height is x x2, and the volume of the solid is: Note that the two integrals in the previous sum were calculated previously: (13 points)