Using a Change of Variables, the Double Integral $\iint$ _{R $\frac { x y } { 1 + x ^ { 2 } y ^ { 2 } } d A$}

Multiple Choice

Using a change of variables, the double integral $\iint$ _{R $\frac { x y } { 1 + x ^ { 2 } y ^ { 2 } } d A$} where R is the region bounded by xy = 1, xy = 4, x = 1, and x = 4 is

A) $\frac { \ln \left( \frac { 15 } { 2 } \right) \ln 4 } { 2 }$
B) $- \frac { \ln \left( \frac { 15 } { 2 } \right) \ln 4 } { 2 }$
C) $\frac { \ln \left( \frac { 13 } { 2 } \right) \ln 4 } { 2 }$
D) $\frac { \ln \left( \frac { 17 } { 2 } \right) \ln 4 } { 2 }$
E) $- \frac { \ln \left( \frac { 17 } { 2 } \right) \ln 4 } { 2 }$