My input:
FullSimplify[Integrate[b1[k], {k, 0, x}] + Integrate[-b1[k], {k, 0, x}]]
computes to:
But I would expect: 0
Do I have to make some assumptions in order to get this to work?
Thanks!
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1 Answer
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I don't know why FullSimplify does not employ the sum rule for this but as a workaround, you could implement your own TransformationFunction:
IntSumTransformFunction[expr_]:=expr/.((Integrate[leftArg1_,rightArg_]+Integrate[leftArg2_,rightArg_]):>Integrate[leftArg1+leftArg2,rightArg])
FullSimplify[Integrate[b1[k],{k,0,x}]+Integrate[-b1[k],{k,0,x}],TransformationFunctions->IntSumTransformFunction]
0
It can even handle "more complicated" cases:
FullSimplify[Integrate[2*b1[k],{k,0,x}]+Integrate[-b1[k],{k,0,x}],TransformationFunctions->IntSumTransFormFunction]
Integrate[b1[k],{k,0,x}]
answered Jul 19, 2017 at 20:28
In[293]:= b1[k_] := k*RandomInteger[{0, 100}]In[293]:= b1[k_] := k*RandomInteger[{0, 100}] Integrate[b1[k], {k, 0, x}] + Integrate[-b1[k], {k, 0, x}] Out[294]= -11 x^2 Integrate[b1[k], {k, 0, x}] + Integrate[-b1[k], {k, 0, x}] Out[294]= -11 x^2$\endgroup$