I think I'm getting the hang of evaluating integrals, but I just wanted to check my answer. Is someone able to confirm if this working and result are correct?

Let

Substituting values gives:

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- May 28th 2009, 05:56 PMdrew.walkerEvaluating definite integral of ln(x)/x from 1 to e
I think I'm getting the hang of evaluating integrals, but I just wanted to check my answer. Is someone able to confirm if this working and result are correct?

Let

Substituting values gives:

- May 28th 2009, 06:10 PMSampras
- May 28th 2009, 06:20 PMdrew.walker
hmmm, so the interval of the integral changes with the substitution? Is there a name for this or somewhere where I can see more examples that you know of?

- May 28th 2009, 06:28 PMdrew.walker
Also, if it's from 0 to 1, ln(1) = 0 and ln(0) is undefined, therefore the answer would now be 0. Is that right?

- May 29th 2009, 04:21 AMmr fantastic
You are getting things mixed up and confused. When making a substitution in a definite integral, you can either:

1. Change the integral terminals and then evaluate the new definite integral: , or

2. Get the anti-derivative in terms of the new variable, re-substitute to get the anti-derivative in terms of the old variable and then evaluate the definite integral in terms of the old variable: .

You do one or the other. You're mixing both together.

The correct answer is 1/2:

1. .

2. .

NO!