consider we want to integrate -1/(y-10)

what I would personally do is pull the (-1) out of the integral sign and integrate 1/(y-10), giving me an answer of -ln(y-10)

the book i'm using//wolfram alpha instead multiplies top and bottom by (-1), changing it to 1/(10-y) and yielding an answer of -ln(10-y)

Why is this? I don't think we can say -ln(10-y) = -ln(y-10)

but at the same time, whichever you choose to derive will get you an answer of 1/(10-y)

what is going on here

thats cause the integral isnt -ln(10-y) its ln(10-y).

you also cannot pull the -1 out without distributing it to the denominator either. when you distribute it, itll give the answer you have when you multiply top and bottom by -1

see what im sayin

This post was edited by Genky on Aug 17 2014 11:23pm

wolfram alpha disagrees with you

edit: link wont work

This post was edited by CrackerJacker on Aug 17 2014 11:26pm

damn thats pretty hard, im good in math and physics but this is nuts

I can rewrite it as (-1) * 1/(y-10)

with (-1) acting as a constant theres no reason I shouldn't be able to take it outside of the integral

This is true. Your book is not saying that -ln(10-y) = -ln(y-10) because this is not equivalent.

However what it is saying is that -1/(y-10) = 1/(10-y).

Your issue lies when you take the integral of -1/(y-10). The answer isnt so much -ln(y-10) as it is -ln( |y-10| )

The same applies if simplify as your book does to 1/(10-y) Then your integral evaluation is -ln( |10-y| )

Which in turn are equivalent.

Let y = 5

Case 1: -ln( | y-10 | )

-ln ( | 5 - 10 | ) = -ln ( | -5 | ) = - ln (5)

Case 2: -ln ( | 10-y | )

-ln ( | 10-5 | ) = -ln (5)

This post was edited by trojan24 on Aug 17 2014 11:43pm

but this is the issue i am having, depending how I decide to factor my integral I get a completely different answer.. i understand that you can rewite -1/(y-10) as 1/(10-y) but that doesn't explain why they yield completely different integrals =/

it seems that puling the constant -1 out of the integral is an illegal move here and i don't understand why..



This post was edited by CrackerJacker on Aug 17 2014 11:54pm

pmd