According to statistical mechanics, the average speed of molecules in an ideal gas is given by v¯ = 4 √ π m 2rt 3 2 z [infinity] 0 v 3 e −m v2/(2rt) dv, where m is the molecular weight of the gas, r is the gas constant, t is the gas temperature, and v is the molecular speed. by evaluating the improper integral, show that v¯ = r 8rt πm . to make algebra simpler, it is suggested to let m/(2rt) ≡ a and carry out the integral.