Thread: a question involving definite integral of a ln absolute function?

1. a question involving definite integral of a ln absolute function?

hello! I have a question regarding an integral which

int ln(abs(x-1)) dx from 0 to 1

I know that this can be written as int ln(1-x) dx from 0 to 1
I try solving the question but I always obtain and undefined function. Any tips on how to solve this question?

2. Rewrite it as $\displaystyle \int_{ - 1}^0 {\ln (|u|)du}$.

Note that $\displaystyle \int {\ln (|u|)du = u\ln (|u|) - u}$

But take care: that is an improper integral. So use limits.

3. is there a way to do it without improper integrals because we didn't learn those yet.

4. Originally Posted by Solid8Snake
is there a way to do it without improper integrals because we didn't learn those yet.
No. And that being the case, I suggest you wait until after you have been taught about improper integrals before attempting the question. (Of course, you can always self-learn by reading ahead in the textbook)