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Student Support Forum: 'Reduced question of last one' topicStudent Support Forum > General > "Reduced question of last one"

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Author Comment/Response
Nasser M. Abbasi
11/14/12 8:27pm

Why the out put of:

Simplify[Integrate[f[x, z] Sin[\[Theta]], {z, 0, 1}] -
Sin[\[Theta]] Integrate[f[x, z] , {z, 0, 1}]]

is not 0?

How to let the out put=0?
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Becuase f[x,z] is not defined, hence it could evaluate to anything. Hence integrand can be anything and Mathematica can't extract Sin[] out before hand.

To force the simplication you want, you need to add an explicit rule to help Integrate.

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Unprotect[Integrate];
Integrate[any_*f_,dom_]:=any*Integrate[f,dom];
Protect[Integrate];

Integrate[f[x,z] Sin[theta],{z,0,1}]-Sin[theta] Integrate[f[x,z],{z,0,1}]

0
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However, the above is not a robust thing as it stands (it can be made more robust, since if `any` happened to be a function of `z`, then you do not want that removed out from the integration.

So, the above assumes that the multiplier inside the integrand does not depend on the integraion parameter.


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Subject (listing for 'Reduced question of last one')
Author Date Posted
Reduced question of last one Xizheng 11/10/12 05:51am
Re: Reduced question of last one Chenyu Lue 11/14/12 03:56am
Re: Reduced question of last one Bill Simpson 11/14/12 6:17pm
Re: Reduced question of last one Nasser M. Ab... 11/14/12 8:27pm
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