MATH 265 Midterm: MATH 265 Iowa State 265F13PT2

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

Document Summary

11/8/2013: evaluate the given integral by changing to polar coordinates d by the semicircle x = 4 y2 and the y-axis. e x2. Y2 da, where d is the region bounded: sketch the region of integration of the following integral and change it to polar coordinates. [hint: use a circle such that the point p corresponds to the origin: exchange the order of integration of the given integral as indicated. Z2 f (x, y, z) dx dz dy to an integral with dv = dz dy dx: 1. 0 f (x, y, z) dz dy dx to an integral with dv = dy dx dz. 5 set up (do not solve) a triple integral in cylindrical coordinates that represents the volume of the solid bounded below by the paraboloid z = x2 + y2 and above by the paraboloid z = 8 x2.