# Question:Why is Maple unable to numerically evaluate this integral?

## Question:Why is Maple unable to numerically evaluate this integral?

Maple

I am new to Maple. I am trying to numerically evaluate the following function with respect to the 3 variables "xop", "yop", and "tp". All other variables appearing in the function f are known (i.e. "x", "y", "z", "Pe", also "Pi" is the constant 3.1415...). "f" is shown below:

f := exp(-1/2*(xop^2+yop^2))*exp(-((x-xop-2*Pe*(t-tp))^2+(y-yop)^2+z^2)/(4*(t-tp)))/((4*Pi^(3/2))*(t-tp)^(3/2))

I am then defining "deltaT" as equal to the triple integral below:

deltaT := int(f, [yop = -(-xop^2+1)^(1/2) .. (-xop^2+1)^(1/2), xop = -1 .. 1, tp = 0 .. t])

When I try to evaluate this, Maple spits out an incredibly long answer full of variables and error functions:

deltaT := -0.7957747155e-1*(int(sqrt(5.-1.*tp)*(int(exp((0.5000000000e-2*(-200.*tp^2*xop^2+40000.*tp^3-4000.*tp^2*xop+2200.*tp*xop^2-617200.*tp^2+41860.*tp*xop-6050.*xop^2+3.170694*10^6*tp-109230.*xop-5.423499*10^6))/((-11.+2.*tp)*(-5.+tp)))*(erf((.1000000000*(10.*sqrt(-1.*xop^2+1.)*tp-55.*sqrt(-1.*xop^2+1.)-3.))/(sqrt(11.-2.*tp)*sqrt(5.-1.*tp)))+erf((.1000000000*(10.*sqrt(-1.*xop^2+1.)*tp-55.*sqrt(-1.*xop^2+1.)+3.))/(sqrt(11.-2.*tp)*sqrt(5.-1.*tp)))), xop = -1 .. 1))/((5-tp)^(3/2)*sqrt(11.-2.*tp)), tp = 0 .. 5))

Any help on figuring out why it is unable to numerically evaluate would be appriciated!

Thanks.

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