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# (or 6thform) Maxwell Speed Distribution?! watch

1. I'm asked to show that the root mean squared speed equals ... using a standard integral. I've been given an equation for f(v). (I can attach a photo later if it'll help)

However, I do not understand why:
<v^2> = inegrate[(v^2)*f(v)]dv
... the limits being infinity and 0. ('integrate' is where the integral symbol is meant to be)

Why does the mean square speed, <v^2>, equal that integral? Is there a derivation to prove this? It's just not making sense.

I've got this identity:
<x^2> = integrate[(x^2)*P(x)]dx

I substituted v for x, dv for dx, and thus P(x) would be replaced by P(v)..which in turn is f(v). BUT P(v) does NOT equal f(v)...does it..which is why I don't get how to use this indentity to get the equation at the top!

Thank you!
2. For any discrete variable .
Extending this to a continuous variable, . The summation or integral is over all possible values of x, denoted by , but the function likely will equal 0 for some of these values.
Replace the x by v2
3. (Original post by morgan8002)
For any discrete variable .
Extending this to a continuous variable, . The summation or integral is over all possible values of x, denoted by , but the function likely will equal 0 for some of these values.
Replace the x by v2
Somehow it all makes sense with that now!! Cheers
4. (Original post by PhysicsGal)
Somehow it all makes sense with that now!! Cheers
You're welcome.

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Updated: January 10, 2015
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