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strange behaviour of Integration

• To: mathgroup at smc.vnet.net
• Subject: [mg88934] strange behaviour of Integration
• From: "Jaccard Florian" <Florian.Jaccard at he-arc.ch>
• Date: Wed, 21 May 2008 14:53:36 -0400 (EDT)

Dear All,

Assuming[0 < a < b,2*Pi*Integrate[y*2*Sqrt[a^2 - (y - b)^2],{y, b - a, b
+ a}]]

gives 2*a^2*b*Pi^2

So does

Assuming[0 < b < a,2*Pi*Integrate[y*2*Sqrt[a^2 - (y - b)^2],{y, b - a, b
+ a}]]

And

Assuming[a < b < 0,
   2*Pi*Integrate[
       y*2*Sqrt[a^2 - (y - b)^2],
       {y, b - a, b + a}]]
Gives

-2*a^2*b*Pi^2

So why does

Assuming[{Element[a, Reals],
     Element[b, Reals]},
   2*Pi*Integrate[
       y*2*Sqrt[a^2 - (y - b)^2],
       {y, b - a, b + a}]]

Give 0 ?

Is this a bug ?

Regards

F.Jaccard