Re: Difference between the following integrals....

*To*: mathgroup at smc.vnet.net*Subject*: [mg66149] Re: [mg66134] Difference between the following integrals....*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Mon, 1 May 2006 01:30:35 -0400 (EDT)*References*: <200604300821.EAA17220@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On 30 Apr 2006, at 17:21, ashesh wrote: > 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. > Look carefully at your definition of f3. {p, -2, -2} ? Andrzej Kozlowski Tokyo, Japan