Definite integration yields a strange answer. (Solved)

[Aries]

(01-31-2019 12:51 AM)Joe Horn Wrote:  

(01-30-2019 08:21 PM)Aries Wrote:  Why x^(1/3) is a complex number if x<0 ?
q is odd …

Simple answer: Graph all three cube roots, and you'll see why.

More complete answer: Because (1) every non-zero number has three distinct cube roots, and (2) calculators which allow complex results return the "principal root" which is the one with the least ARG (that is, the smallest angle from the real axis). The ARG of the real cube root of a negative number is 180°, but the ARG of one of the complex cube roots is 60°, which makes it the principal root.

Yes … I got it now … thanks son … just applied De Moivre and trigonometric form (polar form) of z … but y'know … Id have liked complex and real into separate "domains" … like in the Nspire CAS … just saying … @pwarmuth is right being puzzled … in my view …
Best,

Aries