 
Summary: SUPPLEMENTARY REVIEW PROBLEMS
FOR THE SECOND MIDTERM EXAM
MATH 2573H, FALL 2011
UNIVERSITY OF MINNESOTA
ANSWER KEY
GREG W. ANDERSON
Problem 1
Let Rxy be the quadrilateral in the xyplane with vertices
(0, 0), (2, 1), (1, 2) and (3, 3).
(i) Draw the quadrilateral Rxy carefully, and find the equations of all the lines
forming its boundary.
(ii) Express the double integral Rxy
f(x, y) dx dy as an iterated integral. You
can use either order of integration. And since I did not give you a specific integrand,
I'm not expecting you to evaluate the integralyou can stop after setting up.
Now consider the transformation
T(u, v) =
u + 2v
2u + v
.
