Setting up double integral for polar coordinates and integrating

[bradboynes]

Link:

http://imageshack.us/photo/my-images/39/18463212.jpg/

This is a very long problem so I drew it to make things simpler.

Part a) tells me to set up a double integral in polar coordinates giving the total population of the city.

I have the following:
2π...4
∫...∫ δ(r, θ) r dr dθ. Is this correct?
π/2...1

For part b) I was plugging in numbers, but I feel it can be both i) and ii). Can someone help me figure this out?

For part c) all I would need to do is use what I find in part b) as the integrand for the double integral in part a).

Thank you!

 

[bradboynes]

If anyone can help me, I would be greatly appreciated.

 

[SammyS]

The upper limit of integration for θ is wrong.

 

[bradboynes]

How is it wrong? if you look at it from the side, it should be from pi to pi/2. along the x-axis it's 0 degrees.

 

[Jaynte]

Shouldn't it be from pi/2 to 3pi/2?

 

[SammyS]

It appears that Jaynte is correct.

In which case you should be able to choose between i & ii for pat (b).

 

[SammyS]

Yes: The population density, δ, decreases the farther you live from the shoreline.