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Re: Difference between the following integrals....


On 4/30/06 at 4:21 AM, ashesh.cb at gmail.com (ashesh) wrote:

>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}]

I assume there is a typo here and you actually did
Integrate[f1, {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}]

<snip>

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

Look at the integration limits you set for p. They run from -2 to -2 causing the answer to be zero. I assume you meant to have the integration limits set to run from -2 to 2. Making that change results in the same answer as the other methods.
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