I'm trying to find the integral from -1 to 0 of 1/x^(1/3). Calculators show the answer to be -3/2, but I keep ending up with 0 - (3(-1)^(2/3))/2, which seems to be an irrational number. What am I missing here?

Question

I'm trying to find the integral from -1 to 0 of 1/x^(1/3). Calculators show the answer to be -3/2, but I keep ending up with 0 - (3(-1)^(2/3))/2, which seems to be an irrational number. What am I missing here?

Answer 1

integral x^(-1/3) dx

yes (3/2) x^(2/3) at x =0 - at x = 1

at x = 0 , (3/2) 0^(2/3) = 0
at x = -1 , (3/2) (-1)^(2/3) = 3/2
subtract
-(3/2)

note -1^2 = +1 and +1^(1/3) = 1