Finding the Area Under f(x) with Definition 2

[phillyolly]

Homework Statement

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

Homework Equations

See the attachment for the Definition 2.

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

 

[Mark44]

Homework Statement

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

Homework Equations

See the attachment for the Definition 2.

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

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.

 

[phillyolly]

Is this the correct answer to the problem?

 

[phillyolly]

Actually, I think this is a right answer.

 

[vela]

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

 

[phillyolly]

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

 

[vela]

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

 

[phillyolly]

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

 

[vela]

In the denominator, you didn't use the correct expression for x_i.

 

[phillyolly]

I admire your attention to detail. Thank you a lot.

 

[Mark44]

Being good at mathematics requires attention to detail.