Maxwell-Boltzmann distribution help

[Lily Wright]

Homework Statement

Use the Maxwell-Boltzmann distribution of speeds to find the fraction of F₂ molecules at 500 K which have speeds in the range 240 to 250 m s ^-1
(HINT: determine the fraction of the total area under the distribution curve represented by the part between these two speeds. Assume that the distribution curve is linear over this small range)

Homework Equations

The Attempt at a Solution

So I'm guessing I want to integrate this equation between 240 and 250 m s^-1
So it simplifies to ∫v²e^-mv2/2KTdv
I'm not very good at integrating so I genuinely have no idea what happens after that

 

[Redbelly98]

Homework Statement

Use the Maxwell-Boltzmann distribution of speeds to find the fraction of F₂ molecules at 500 K which have speeds in the range 240 to 250 m s ^-1
(HINT: determine the fraction of the total area under the distribution curve represented by the part between these two speeds. Assume that the distribution curve is linear over this small range)

Homework Equations

The Attempt at a Solution

So I'm guessing I want to integrate this equation between 240 and 250 m s^-1
So it simplifies to ∫v²e^-mv2/2KTdv
I'm not very good at integrating so I genuinely have no idea what happens after that

You don't have to integrate if you use the given hint: "Assume that the distribution curve is linear over this small range"

 

[Lily Wright]

Ah ok so would I just work it out for each velocity?

 

[Redbelly98]

Yes.