MTH 162 Midterm: MTH 162 University of Rochester Fall 13Exam2 Solutions

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

Document Summary

November 14, 2013: (20 points) consider the curve f (x) = x4. 1 x3 , the arc length function is given by. 32: (20 points) (a) find the area of the surface of revolution obtained by rotating the curve y = x2, for. 0 x 2, about the y-axis. Math 162 (calculus iia) (b) find the area of the surface of revolution obtained by rotating the curve x = 1 + |y|, for. 1 y 1, about the y-axis. Setting u = 1 + 4x2, we have du = 8xdx, so that xdx = du/8. Also when x = 0, we have u = 1, and when x = 2, u = 17. 4 (cid:20) 2 if y 0, if y < 0, and therefore dx dy. 1 if y 0, if y < 0. 2 (1 + |y|)p1 + (dx/dy)2dy (1 y)p1 + ( 1)2dy + 2 z 1.