MATH 241 Midterm: MATH241_ROSENBERG-J_FALL2010_0101_MID_SOL_2

• School: University of Maryland
• Department: Mathematics
• Course: MATH 241
• Professor: ALL

Document Summary

Math 241, 4th examination, solutions and grading key. Monday, december 6, 2010: (25 points) compute the area of the region in the rst quadrant bounded by the coordinate axes and the curve x2/3 + y2/3 = 1. Hints: try the change of variables x = u cos3(v), y = u sin3(v). If you end up with an integrand involving sin(v) cos(v), recall that this is 1. If x = u cos3(v), y = u sin3(v), then. = 3u sin2(v) cos(v) (5 for the derivatives). In the new coordinates, the x-axis becomes v = 0, the y-axis becomes v = /2, and the curve x2/3 + y2/3 = 1 becomes u2/3 cos2(v) + u2/3 sin2(v) = u2/3 = 1, or u = 1. The origin becomes u = 0 (5 for the new bounding curves). 3u cos2(v) sin2(v) du dv (20 to here) cos2(v) sin2(v) dv!