Timeline for Integral of real function is complex
Current License: CC BY-SA 4.0
7 events
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| Jul 31, 2023 at 17:31 | vote | accept | korni1990 | ||
| Jul 31, 2023 at 16:28 | answer | added | Andreas | timeline score: 3 | |
| Jul 31, 2023 at 13:33 | comment | added | josh |
The integrand is not real. It's multivalued (like $z^{1/3}$ is). The discontinuity arises from integrating it using a multivalued antiderivative over a path which is not analytically continuous, that is, across its branch point at the origin. Look at ComplexExpand[x^(2/3)/(-x)^(2/3)] and note how the argument of x abruptly changes from $0$ to $\pi$ across the branch point as $x$ changes from negative to positive giving rise to the discontinuity.
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| Jul 31, 2023 at 12:48 | comment | added | Nasser | If differentiating the anti derivative gives back the integrand ($\pm$ constant in anti is OK), then the result is correct, which is in this case. !Mathematica graphics | |
| Jul 31, 2023 at 12:47 | comment | added | Domen |
Integrate[E^x x^(2/3), {x, 0, x}]
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| Jul 31, 2023 at 12:44 | comment | added | Ulrich Neumann | Your function isn't real for x<0! | |
| Jul 31, 2023 at 12:32 | history | asked | korni1990 | CC BY-SA 4.0 |
