MATH 265 Midterm: MATH 265 Iowa State Exam265F10FSolutions

• School: Iowa State University
• Department: Mathematics
• Course: MATH 265
• Professor: All

Document Summary

Answers without procedure will be penalized with loss of points. Use the change of variables u = y + 1. 2 x to rewrite (including new limits) the integral rrr(2y + x)2 da, where the region r in the xy-plane is the parallelogram bounded by the four lines as in the gure below. (5 pts) 4. Write an iterated integral (do not evaluate) that describes the volume of the solid enclosed by y2 = x, z = 0 and x + z = 1. if dv = dz dy dx. (10 pts) 5. Assume its density is given by some (x, y, z). Evaluate a triple integral to nd the mass of a solid with density (x, y, z) = 3, that is bounded by the surfaces: z = x2 + y2, x2 + y2 = 9 and z = 1. [for 5 extra credit points nd the center of mass of this same solid!]