Finding the number of stars in the milky way

[BOAS]

Homework Statement

The Milky Way contains 100 billion stars. The present masses of stars in the Milky Way are distributed according to dN/dm ∝ m−2 , and that stars have masses between 0.1 M and 100 M

M = Solar mass

Determine the number of stars with masses greater than or equal to the Sun.

Homework Equations

The Attempt at a Solution

$\frac{dN}{dm} ∝ m^{-2}$

$\frac{dN}{dm} = k m^{-2}$

$dN = k m^{-2} dm$

$\int^{100 \times 10^{9}}_{0} dN = \int^{100M}_{0.1M} k m^{-2} dm$

N = 100 billion, but I'm just leaving it as N for now.

$N = - \frac{K}{m}|^{100M}_{0.1M}$

$N = \frac{999K}{100M}$

I am a bit confused about the physical meaning of this and where to go next...

Do I use this to find a numerical answer for K and then integrate again between 1 solar mass and 100 solar masses to find the number of stars in the milky way with greater or equal mass?

Thanks for any help you can give!

 

[phyzguy]

Do I use this to find a numerical answer for K and then integrate again between 1 solar mass and 100 solar masses to find the number of stars in the milky way with greater or equal mass?

Yes. You're on the right track. Just keep going.