The population density of a certain city is given by the function where the origin (0, 0) gives the location of the government center.Find the population inside the rectangular area described by

Question

The population density of a certain city is given by the function  where the origin (0, 0) gives the location of the government center.Find the population inside the rectangular area described by

Quizplus · Accepted Answer

To find the population inside the rectangular area, we need to integrate the given function over the range of x and y values specified in the rectangle. 
Integrating the function from x = -3 to x = 3 and from y = -2 to y = 2 gives:
∫(-3 to 3)∫(-2 to 2) (11e^(-0.2(x^2+y^2))) dy dx
This integral can be solved using polar coordinates: 
∫(0 to 2π)∫(0 to 2) (11e^(-0.2r^2)) r dr dθ
Solving this integral gives the population inside the rectangular area as approximately 9.97. 
The closest answer choice is B, 11eb12b0_a91f_321d_b394_a9d77ec13b9a_TB7866_11, which is approximately 9.96.

The Population Density of a Certain City Is Given by the Function