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## Homework Statement

Assume the Milky Way contains about 3 × 10^11 stars that were formed all at once,

with an initial mass function:

[tex]\frac{dN}{dM}\propto M^{-2.35}[/tex]

in the range 0.1–100 solar masses.

How many stars in the Galaxy are less massive than the Sun? How much mass

do these stars make up? What fraction of the total stellar mass is it?

## Homework Equations

[tex]N_{total}= \int \frac{dN}{dM} dm[/tex], with an upper limit of 100 solar masses, and a lower limit of .1 solar masses.

## The Attempt at a Solution

Since dN/dM is proportional to M^-2.35...

Set the integral up as...

[tex]3x10^{11}=\int CM^{-2.35} dm[/tex], with the same boundaries as before, 100, and .1.

Solving for C, i got 1.81x10^10.

Changing the boundaries to 1 solar mass and .1 to find how many stars have a mass lower than the sun i got..

N= 1.81x10^10[-.741+16.6] = 2.86x10^11 stars

Now where im having trouble is finding the mass fraction. The total mass would just be the sum of the mass of all the stars, but im having trouble figuring out how to manipulate the integral to give me the total mass. Any help is appreciated.

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