Help with Calc Homework!
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Help with Calc Homework!

[From: ] [author: ] [Date: 11-10-21] [Hit: ]
......
v=4/sqrt(pi)*((M/2RT)^(3/2))*(Integral of (v^3)(e^(-Mv^2/2RT)) from 0 to infinity)

Prove v=sqrt(8RT/piM)

-
u = Mv^2 / (2RT) ---> v^2 = (2RT/M) u
(RT/M)du = v dv

v^3 dv = v^2 v dv = (2RT/M) u (RT/M)du = 2(RT/M)^2 u du

so your integrand becomes

(v^3)(e^(-Mv^2/2RT) dv = 2(RT/M)^2 u e^{-u} du

Can you do it now?
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