Change the Cartesian Integral to an Equivalent Polar Integral, and Then

Multiple Choice

Change the Cartesian integral to an equivalent polar integral, and then evaluate.
- $\int _ { - 9 } ^ { 0 } \int _ { - \sqrt { 81 - x ^ { 2 } } } ^ { 0 } \frac { 1 } { 1 + \sqrt { x ^ { 2 } + y ^ { 2 } } } d y d x$

A) $\frac { \pi ( 9 + \ln 10 ) } { 2 }$
B) $\frac { \pi ( 9 + \ln 10 ) } { 4 }$
C) $\frac { \pi ( 9 - \ln 10 ) } { 4 }$
D) $\frac { \pi ( 9 - \ln 10 ) } { 2 }$