# Homework Help: Integral problem.

1. Jul 18, 2010

### phillyolly

1. The problem statement, all variables and given/known data

Use Definition 2 to find an expression for the area under the graph of f as a limit. Do not evaluate the limit

f(x)=(lnx)/x

3 ≤ x ≤ 10

2. Relevant equations

See the attachment for the Definition 2.

3. The attempt at a solution

∫ ln(x) / x dx = 1/2 (ln(x))² + C

10
∫ ln(x) / x dx = 1/2 [ (ln(10))² - (ln(3))² ]
3

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2. Jul 18, 2010

### Staff: Mentor

You are supposed to actually use Definition 2, meaning that you are supposed to write the integral as the limit of a summation. The purpose of this exercise is NOT to get a numerical value for the integral.

3. Jul 18, 2010

### phillyolly

Is this the correct answer to the problem?

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4. Jul 19, 2010

### phillyolly

Actually, I think this is a right answer.

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5. Jul 19, 2010

### vela

Staff Emeritus
Almost, but not quite. Show us how you got that. Tell us what you used for Δx and xi first, and show us how you got the summation after you plugged everything in.

6. Jul 19, 2010

### phillyolly

OK, I think I got a mistake. Is that correct now?

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7. Jul 19, 2010

### vela

Staff Emeritus
Closer. You forgot the factor of Δx in the summation, and you made an algebra error.

8. Jul 19, 2010

### phillyolly

I see I forgot the factor of Δx. I don't see an algebra error :(
Olga

9. Jul 19, 2010

### vela

Staff Emeritus
In the denominator, you didn't use the correct expression for xi.

10. Jul 19, 2010