Question

how to deal with this absolute value.

Answer 1

\[\int\limits_{0}^{2} \frac{dx}{\sqrt{|x-1|}}\]

Answer 2

I tried a u substitution u = sqrt{|x-1|}

so u^2 = |x-1|

then 2udu = dx

Answer 3

gonna need to separate integrals buddy

Answer 4

x is negative from 0-1 so do the same integral from 0 to 1 and make it positive and then add it to the integral from 1-2

Answer 5

\[\int\limits_{0}^{2} \frac{2udu}{u}\]

Answer 6

also make the U substitution just (x-1) so then you can have u^-1/2

Answer 7

Split the integral into 2 parts. Between 0 and 1, |x-1| =1-x and between 1 and 2 |x-1|=x-1

Answer 8

oh I see so let me separate it and add a - sign like