You are Here: Home >< Maths

# Why do you use modulus with ln when integrating? C4 watch

1. Can someone please explain why we use the modulus in the ln when integrating. The book says that the reason for this is explained in 6.5 however it doesn't say anything.

THanks mike
2. who is mike?
3. Because the natural log of non-positive numbers is not defined, and ln|x| = lnx if x > 0, with derivative 1/x, but ln|x| = ln(-x) if x < 0, with derivative -1(1/-x) = 1/x
4. (Original post by michael242103)
Can someone please explain why we use the modulus in the ln when integrating. The book says that the reason for this is explained in 6.5 however it doesn't say anything.

THanks mike
(Original post by 13 1 20 8 42)
Because the natural log of non-positive numbers is not defined, and ln|x| = lnx if x > 0, with derivative 1/x, but ln|x| = ln(-x) if x < 0, with derivative -1(1/-x) = 1/x
As he said, the natural log of non-positive numbers is not defined. You might still question why it's okay to just throw a modulus on it though.

One reason is because ln(-x) + c= ln(-1) + ln x + c = ln x + k where k = c + ln(-1) since ln(-1) is just a constant. (it's actually ipi). So in the end you get ln x anyway. That justifies you throwing on the modulus signs.
5. (Original post by TeeEm)
who is mike?
me mate
6. (Original post by GeologyMaths)
me mate
were you not banned? (again?)
7. (Original post by TeeEm)
were you not banned? (again?)
dont even start mate
8. so try and draw the graph baby

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: January 29, 2016
Today on TSR

### Life lessons uni will teach you

Questionable decision-making and constant surprises

### University open days

1. Loughborough University
Fri, 21 Sep '18
2. University of Cambridge
Fri, 21 Sep '18
3. Richmond, The American International University in London
Fri, 21 Sep '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams