MATH 265 Midterm: MATH 265 Iowa State Midterm3 2011

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

Document Summary

This test is closed book and closed notes. For full credit show all of your work (legibly!). Each problem is worth 10 points (a total of 50 points): rewrite. 0 f (x, y) dy dx +z 1. 0 f (x, y) dy dx +z 2. 1 f (x, y) dy dx as a single integral of the form. If we sketch the region that the three integrals corresponds to, we see that we are bounded by the lines y = 0, y = 3, y = 3 + 3x and y = x2 1. The last two we can rewrite as x = (1/3)y 1 and x = y + 1 (we take the positive square root because we want the right hand side, i. e. , positive x-values). It is now easy to set up the desired integral and we have. Z 3 (1/3)y 1 f (x, y) dx dy.