Integral NA in home, CAS

[Han]

(02-29-2016 01:23 PM)parisse Wrote:  For the part in -1..0, the correct answer is 1-i, with the complex definition of the fractionnal power. If you add the 0..1 part, you get 2*sqrt(2)-i as stated by compsystem.
If you take the nthroot instead of the complex fractional power on -1..0, then x "power" -2/3 is negative and smaller than -1, adding 1 will return a negative number, taking the square root a pure imaginary, and the integral is
int (sqrt (1-(-x)^(-2/3)),x,-1,0)=i
Therefore the values reported by lrdheat on the nspire and classpad are wrong, either there is a bug on these calcs, or lrdheat made an input error.
Just curious: where does this integral come from? If it's from a textbook, I really wonder what the author wanted to check...

Perhaps I am misreading your post, but for \( x \in [-1,0] \), \( x^{-2/3} \) would be positive due to the 2 in the exponent (if not using the complex fractional power). These other calculators are computing the integral as follows:

https://www.wolframalpha.com/input/?i=in...)),x,-1,1)

Their algorithms may possibly be using the even-ness of the integrand since the integral is an improper integral.