What is the Calculation for the Number of Stars in the Solar Neighborhood?

[Fox]

I'll admit, I'm fried. If I can just solve this one problem before the end of the night, I'll be golden though. All help is appreciated... the wording is a bit tricky, which is killing me.

The "solar neighborhood" can be defined as all the stars of the galaxy within a radius of 100 parsecs (pc.) of the sun. The region of the galaxy near the sun can be represented by a disk, where the density of the stars is constant in the central xy plane of the disk but varies as:

D = D(o) * exp (-|z|/B)

normal to the central plane of the disk. D(o) = 1/9 pc^-3 and B = 500 pc is the effective half thickness of the disk. Use cartesian coordinates to calculate the number of stars in the solar neighborhood. Hint: Do the y integral first and the z intergral last.

If someone could even give me any sort of hint on how to set this things up (ex. The intergration) it would help greatly. This is the last problem of the year... and I'm fried... and can barely think.

 

[whozum]

The integral in the y direction is constant, in the z direction it is variable though, this is obvious in the function. You are just integrating a sphere with radius 100 parsecs, the integrand is the above function.

edit: cylinder, not sphere.

 

[Fox]

Have to admit, I don't get it.

Do I just intergrate D(o)*e^(|z|/B) dy dx dz ?

Here's the drawing he gave us to go with it. It's a bit blurry, but maybe it'll help more :)

http://i3.photobucket.com/albums/y89/tcnjfox/IMG_0327.jpg

thanks guys :)

 

[Fox]

can anyone help clarify this for me? :)