a question involving definite integral of a ln absolute function?

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September 21st 2010, 10:35 AM
Solid8Snake

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?

Thanks in advance!
September 21st 2010, 10:53 AM
Plato

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

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

But take care: that is an improper integral. So use limits.
September 21st 2010, 03:43 PM
Solid8Snake

is there a way to do it without improper integrals because we didn't learn those yet.
September 21st 2010, 03:49 PM
mr fantastic

Quote:

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)

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