Wrong integration result with R2011b

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Daniel
Daniel 2012-3-27
I get a wrong result with R2011b when doing the folloing integration:
>> syms x
>> syms a
>> int(x/2+sin(2*a*x)/(4*a),x)
ans =
x^2/4 - cos(a*x)^2/(4*a^2)
>> int(x/2,x) + int(sin(2*a*x)/(4*a),x)
ans =
x^2/4 - cos(2*a*x)/(8*a^2)
So the second result is the correct one, the first is wrong (when transforming the second result to the form of the first one there is a -1/(8*a^2) missing). When using R2010b I get the correct result when calculating int(x/2+sin(2*a*x)/(4*a),x). Is this a bug in R2011b?
  1 个评论
Jan
Jan 2012-3-27
Does this mean, that you are missing a constant expression after calculatingthe integral?

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Alexander
Alexander 2012-3-27
Both answers are correct. Let me quote Wikipedia's entry for Constant of integration:
In calculus, the indefinite integral of a given function (i.e., the set of all antiderivatives of the function) is only defined up to an additive constant, the constant of integration.
Since -1/(8*a^2) does not depend on x it is just another constant of integration. You can also verify this if you derive both results with respect to x.

更多回答（1 个）

Daniel
Daniel 2012-3-27
Yes, you are right, I didn't take that into account, thanks!
Still, I find it strange, that there are different results for different version, but now that I recognized that everything is fine, I can live with it.

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