Mathematics
OpenStudy (anonymous):

evaluate ⌠1 (x-x^2)/(2*x^(1/3)) ⌡-8 (the signs with 1 and -8 is supposed to be an integral sign... w/ upper and lower bounds 1 & -8 respectively)

OpenStudy (anonymous):

Divide the x^(1/3) through the numerator. Then integrate term by term.

OpenStudy (anonymous):

$\int_{-8}^1\frac{x-x^2}{2x^{\frac{1}{3}}}dx$

OpenStudy (anonymous):

Pull out the 1/2 then divide all the terms by x^(1/3) giving: $\frac{1}{2} \int\limits x^{2/3}-x^{5/3}dx=\frac{1}{2}(\frac{3}{5}x^{5/3}-\frac{3}{8}x^{8/3})+C$

OpenStudy (anonymous):

Then evaluate it^^

OpenStudy (anonymous):

thanks! but when you plug in -8, i get an undefined number... is it okay to just take that out?

OpenStudy (anonymous):

when you evaluate it, would the answer be -383/10 ?

OpenStudy (anonymous):

H/o I'll tell you

OpenStudy (anonymous):

You actually get a complex answer D:

OpenStudy (anonymous):
OpenStudy (anonymous):

The problem is, you get a discontinuity at x=0. So you have to integrate it from -8 to y then y to 1. Then take the limit as y=>0

OpenStudy (anonymous):

thanks!

OpenStudy (anonymous):

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