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Difference between the following integrals....


Hi all,

Would like to integrate Abs[x]*(x+3y^2) for {x,-2,2} and {y,-1,2}. Have
four different ways of doing this integration as follows:

f1 = Abs[x](x + 3y y);
Integrate[f3, {x, -2, 2}, {y, -1, 2}]

f2[a_, b_] := Piecewise[{{a*(a + 3*b*b), a > 0}, {-a*(a + 3*b*b), a <
0}}]
ii = Integrate[f2[a, b], {a, -2, 2}, {b, -1, 2}]

f3[p_, q_] := Which[p < 0, -p*(p + 3*q*q), p > 0, p*(p + 3*q*q)]
Integrate[f3[p, q], {p, -2, -2}, {q, -1, 2}]

f4 = int_m_-2^0 int_n_-1^2 (-m*(m+3n^2)) dn dm + int_m_-2^0 int_n_-1^2
(m*(m+3n^2)) dn dm

Answers:

f1 = 36

f2 = 36

f3 = 0

f4 = 36

As I understand all these 4 are performing the same operation, but why
does f3 become = 0.

Hope some one can give me an insight into the mistake (please identify
the mistake too for me) I am making here.

Regards.


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