Question

Discworld problem, anyone can help me? T^T

Answer 1

mass of the atmosphere is the density times the volume.
I would use the "disc method"
see
http://www.khanacademy.org/math/calculus/solid_revolution_topic/disc-method/v/disc-method-around-y-axis
or
http://tutorial.math.lamar.edu/Classes/CalcI/MoreVolume.aspx (Example 3)

but you must multiply by the density function while integrating.

Answer 2

my prof expressed it in riemann sums.. ):

Answer 3

this is actually the solution but i dont understand it, can anyone please explain T^T

Answer 4

The bottom part shows the integral. The top part is an "explanation" of why the integral idea works.

Answer 5

openstudy is acting flaky today.

Here is the idea:
you have a shape that looks like this