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## Homework Statement

The equivalent of the Maxwell-Boltzman distribution for a two-dimensional

gas is

[itex]P(v) = Cv e^-\frac {mv^2}{kt}[/itex]

Determine [itex]C[/itex] so that

[itex]\int_0^\infty P(v)dv = N[/itex]

## Homework Equations

Not really sure

## The Attempt at a Solution

I wasn't really sure how to tackle this question so I figured i'd integrate [itex]P(v)[/itex] since the question says that'll equal N.

[itex]\int_0^\infty P(v)dv[/itex]

[itex]\int_0^\infty Cv e^-\frac {mv^2}{kt} dv[/itex]

[itex]C\int_0^\infty v e^-\frac {mv^2}{kt} dv[/itex]

[itex] u = \frac {mv^2}{kt}[/itex]

[itex]\frac {du}{dv} = \frac {2mv}{kt}[/itex]

[itex]dv = \frac {du kt}{2mv}[/itex]

[itex]C\int_0^\infty v e^{-u} \frac {du kt}{2mv}[/itex]

[itex]C\int_0^\infty e^{-u} \frac {du kt}{2m}[/itex]

[itex]\frac {Ckt}{2m} \int_0^\infty e^{-u} du[/itex]

[itex] = \frac {Ckt}{2m} \bigg[{-e^{-u}\bigg]_0^\infty[/itex]

[itex] = \frac {Ckt}{2m} \bigg[{-e^{-\frac {mv^2}{kt}}\bigg]_0^\infty[/itex]

I'm not really sure where to go from here. How would I evaluate this between infinity and zero?

Thanks