integral (-inf to inf) [e^(-x^2/2 sigma^2) dx / sqrt(2*pi*sigma^2)] = 1
=> integral (-inf to inf) [e^(-x^2/2 sigma^2) dx] = sqrt(2*pi*sigma^2)
=>integral (0 to inf) [e^(-x^2/2 sigma^2) dx] = sqrt(2*pi*sigma^2)/2
=> integral (0 to inf) [e^(-c*x^2) dx] = sqrt(pi/c)/2

Because, probability function,
f(x) ...

Solution Summary

The solution discusses (Ross # 5.1 - Theoretical) The speed of a molecule in a uniform gas at equilibrium is a random variable whose probability density function is given by ....

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...Molecules with different speeds would hit the disk at ... of a material that will cause the molecules hitting it ... the disk one can then deduce the speed distribution ...

... Each hailstone has a mass m and a speed v. If the collisions are elastic ... total kinetic energy of the gas molecules and the average kinetic energy per molecule. ...