Question: Strange answer in IntegrationTools[Change]

 

restart;

with(IntegrationTools):

# A very simple double integral

J:=Int(Int(x^2, x = 0 .. y), y = 0 .. 1);

Int(Int(x^2, x = 0 .. y), y = 0 .. 1)

(1)

value(J);

1/12

(2)

# Try a simple change of variables

Change(J, x=t*y, [t]);   # Why this form?

Intat(Intat(_a^2, _a = _b)-Intat(_a^2, _a = 0), _b = 1)-Intat(Intat(_a^2, _a = _b)-Intat(_a^2, _a = 0), _b = 0)

(3)

value(%);

1/12

(4)

# Now the same for 2*J

Change(2*J, x=t*y, [t]);  # OK, but why?

2*(Int(y^3*(Int(t^2, t = 0 .. 1)), y = 0 .. 1))

(5)

value(%);

1/6

(6)

 


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