Why is this integral hard for mathematica?
Kristian Schmidt
Consider this indefinite integral: Integrate[Sqrt[
4 k (1 + \[Alpha] (-1 + \[Epsilon])) + (h + \[Epsilon] -
h \[Epsilon])^2], \[Epsilon]]
This evaluates fine. Now try the same integral with limits of 1/2 and 3/2:
Integrate[Sqrt[
4 k (1 + \[Alpha] (-1 + \[Epsilon])) + (h + \[Epsilon] -
h \[Epsilon])^2], {\[Epsilon], 1/2, 3/2}]
This hangs, and I haven't been patient enough to wait it out yet :)
k and alpha are just real numbers, and 0<= h <= 1. Adding these assumptions didn't seem to help though.
I cannot see why it hangs. If mathematica is able to compute the antiderivative just fine, isn't it just a matter of substracting the antiderivative with itself in the two limits?
dh
Hi Kristian,
the anti-derivative has branch cuts. In this case you must figure what
branch you have to take. I guess that this is what Mathematica does.
E.g. set h=0.5;k=1;alpha=1 and integrate from 0 to 1
evaluate the integral and you get: 2.216..
now calculate the anti-derivative at 1 and 0 and take the difference,
you get: -1.537.. , this is wrong
Daniel
Kristian Schmidt wrote:
> Hello
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> Integrate[Sqrt[
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