Solve the Problem $\mathrm { f } ( \mathrm { x } , \mathrm { y } ) = ( 3000 \mathrm { e }^ { y } ) / ( 1 + | \mathrm { x } | / 2 )$

Multiple Choice

Solve the problem.
-If $\mathrm { f } ( \mathrm { x } , \mathrm { y } ) = ( 3000 \mathrm { e }^ { y } ) / ( 1 + | \mathrm { x } | / 2 )$ represents the population density of a planar region on Earth, where $\mathrm { x }$ and $\mathrm { y }$ are measured in miles, find the number of people within the rectangle $- 6 \leq x \leq 6$ and $- 4 \leq y \leq 0$ .

A) $12,000 \left( 1 - e ^ { - 4 } \right) \ln 4 \approx 16,331$
B) $6000 \left( 1 - e ^ { - 4 } \right) \ln \frac { 7 } { 2 } \approx 12,248$
C) $6000 \left( 1 - e ^ { - 4 } \right) \ln 4 \approx 8165$
D) $3000 \left( 1 - \mathrm { e } ^ { - 4 } \right) \ln 4 \approx 4083$