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DeMath · #9 January 2nd, 2009, 01:52 PM

Quote:

Originally Posted by Scott H

Are you sure? I thought we had to change the bounds of integration after the change of variables.

Frog09, remember also that $\ln\,u$ is defined as $\int_1^u\,\frac{1}{x}\,dx.$

Yes, I am sure!
In my solution we must not change the bounds of integration.
Because

$\left. {\int\limits_b^a {\frac{{f'\left( x \right)}}{{f\left( x \right)}}dx = } \ln \left( {f\left( x \right)} \right)} \right|_b^a = \ln \left| {f\left( a \right)} \right| - \ln \left| {f\left( b \right)} \right|.$