Why do you Tack on The Negative For this Integral


by bmed90
Tags: integral, negative, tack
bmed90
bmed90 is offline
#1
Feb7-12, 07:59 PM
P: 99
If you integrate

1/(1-y)dy

why do you end up with a negative in front of your answer

-ln|1-y|+c
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Char. Limit
Char. Limit is offline
#2
Feb7-12, 08:01 PM
PF Gold
Char. Limit's Avatar
P: 1,930
Because using u-substitution, we get this:

u = 1 - y, du = - dy

And so...

[tex]\int \frac{1}{1-y} dy = - \int \frac{1}{u} du[/tex]

Integrating the right-hand side, we get - ln|u| + C, or - ln|1-y| + C.
bmed90
bmed90 is offline
#3
Feb7-12, 10:47 PM
P: 99
gotcha


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