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Solving a double integration and feeding function...

Need to solve a double integration:

int_x_0^t int_y_0^t F(x).exp(-a.Abs[x-y]).G(y)dy dx

F(x) = (3x/t)     for 0<x<(t/3)
     = (2t-3y)/t  for (t/3)<x<(2t/3)
     = 0; otherwise

G(y) = F(y);

Is it possible to feed this type if functions which vary depending on
the range of variable (x or y).

Please note that a, t are both real numbers. Further, note the Abs[x-y]
in the exponent.

Thanks in Advance.

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