# Question:Integration incorrect with assume command, correct without assume

## Question:Integration incorrect with assume command, correct without assume

Maple
In trying to answer a question for one of my students I found the following strange behavior: The probability density for the time t that standard Brownian motion started from 0 first hits the value a > 0 is: f := a*exp(-a^2/(2*t))/(sqrt(2*Pi)*t^(3/2)) Then the expected value of this hitting time is: int(t*f, t = 0 .. infinity) Maple 11 gives the answer signum(a)*infinity which is correct, as long as one understands that signum(a)=1. However, if one now assumes that a > 0 and integrates, then the answer is incorrect: > assume(a > 0); > int(t*f, t = 0 .. infinity); 2 -a A Maple 11 worksheet is attached so you can reproduce what I did. I believe there must be something about assume that I am missing here. Does anyone have an explanation? Steve Dunbar View 410_ExpectedHittingTime.mw on MapleNet or Download 410_ExpectedHittingTime.mw
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