@Carl Love 

Hello,

Thank you so much for your explanation!!! Now this issue makes a lot of sense. 

@Kitonum 

Hello,

Thank you for answering my question. If I may follow up with a new equation with the following values for x, y, z, Pe, t,

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

x := 1; y := 2; z := 3; Pe := 4; t := 5;

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

evalf(%)

This integral seems to never finish computing. Let me know if you can talk a look at this one!

Thanks.