MATH 1172 Midterm: MATH 1172 Ohio State University Math 1172 6.4 solutions Fa 2014

• School: Ohio State University
• Department: Mathematics
• Course: MATH 1172
• Professor: All

Document Summary

True: the line x = 3 is parallel to the y-axis. Use the shell method to nd the volume of the solid generated when r is revolved around the x-axis. 1. Solution: as noted by the problem we will use the shell method to nd the volume of this shape. Since we are rotating around the x axis, in order to use the shell method we should integrate over y. The curves x = 4 and x = y2 intersect at the y value 2 and our region is bounded from be- low by the line y = 0. a thus our interval of integration is [0, 2]. The top function is x = 4 and our bottom function is x = y2. b hence. = 8 . anotice that the curves actually enclose two regions, one below the x axis and one above. When rotated around the x axis, each region carves out the same shape.