Re: Integral Message #32 Posted by Bunuel66 on 22 Sept 2013, 1:16 p.m., in response to message #31 by Nigel J Dowrick
Well, if we choose cubic root of x with x<0 as -cubic root abs(x) which means that cubic root of -8 is -2, which is in R then there is no need of any complex value.
The point is that in C cubic root of -1 has 3 possible values:
cos(pi/3)-i.sin(pi/3); -1; cos(pi/3)+i.sin(pi/3)
Then any cubic root of a negative number could be a multiple of those three values.
Depending of the choice the integral will be real or complex. Both results are equally right as long as the hypothesis are clear.
What does the Prime if you plot cubic root of x for x in [-5,5]....?
My two cents...
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