(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Problem:

A (area) = [tex]\int^{e}_{1}[/tex] ln(x) dx = 1

Now we let k be such that 0 [tex]\leq[/tex] k [tex]\leq[/tex]1

Consider the line y = k.

Find k so that area computed by A is exactly one half.

2. Relevant equations

So, first, I found point of intersection:

k = ln (x)

e[tex]^{k}[/tex] = x

Now I have:

1/2 = [tex]\int^{e}_{e^{k}}[/tex] ln (x) dx

3. The attempt at a solution

I'm having a hard time grasping the big picture of this, that's pretty much why I'm stuck. I know that Newton's Method is used to find the roots of a function, but this area twist is really giving me a hard time. I'm supposed to use N.M. to solve for k after setting up integral to compute A/2. THEN I have to experiment to find 2A/3 and A/1000. Can anyone enlighten me? Where is this zero happening?? Am I supposed to use [tex]\int[/tex] ln (x) -k dx??

HELP!!

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# Homework Help: Newton's Method

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