What is the Initial Mass Function Problem?

[kranav]

Homework Statement

Hello! I am currently working on a initial mass problem and getting nowhere, I need a little help here, the question states

consider a newly formed globular cluster, with total mass 10e6 times that of the sun, and an initial mass function dN/dm = a.m(-2.35) (-2.35 being the power of m of course) in the mass range 0.1-20 mass of the sun, where m=M/mass of the sun. find a.

Homework Equations

The Attempt at a Solution

what i did till now is
we know that globular clusters have 10e4 to 10e6 stars so

integral of N(m)dm = 10e6 where m ranges from .1 to 20 mass of the sun
with this equation I got the value of N which was too small and used the given equation dN/dm = a.m(-2.35) to find a. Is this method correct ?
Thanks.

 

[gabbagabbahey]

integral of N(m)dm = 10e6 where m ranges from .1 to 20 mass of the sun
with this equation I got the value of N which was too small and used the given equation dN/dm = a.m(-2.35) to find a. Is this method correct ?
Thanks.

Shouldn't the number of stars in a given mass range $m_1\leq m\leq m_2$ be equal to

$$N=\int_{m_1}^{m_2} dN=\int_{m_1}^{m_2} \frac{dN}{dm}dm$$

?

 

[kranav]

thank you, ill try using this now