Solving Arc Length Integral for y=ln(1-x^2) - 0 to 1/2

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Homework Help Overview

The problem involves finding the length of the curve defined by the function y=ln(1-x^2) over the interval from 0 to 1/2. Participants are discussing the integral setup and the signs involved in the calculations.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are examining the integral for arc length and questioning the signs in the decomposition of the integral. There is mention of confusion regarding the steps leading to the final expression in the solution manual.

Discussion Status

The discussion appears to be ongoing with some participants seeking clarification on specific steps and signs in their calculations. One participant expresses that they have resolved their confusion, while others are still probing the details of the integral setup.

Contextual Notes

There is a noted lack of detailed step-by-step work from one participant, which complicates the ability of others to provide targeted assistance. The discussion is constrained by the need for clarity in the mathematical process involved in the arc length calculation.

hachi_roku
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Homework Statement



ok, the original prob is : find the length of the curve of y=ln(1-x^2) x between 0, 1/2.



Homework Equations





The Attempt at a Solution


ive made it this far: my integral is -1 + 2/1-x^2.....ok so i decompose the second part but in doing so i get a negative to make it -(x+1)(x-1) but i don't know what happens to that negative because the solution manual says the integral is ...-1+ 1/x+1 -1/x-1 dx i don't get the signs. please help!
 
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if we are woking with single variable functions, y=f(x) like here then the arc length from a to be of a curve is:


[tex]L=\int_a^b\sqrt{1+[f'(x)]^2}dx[/tex]
 
yes...like i said I've already worked that part...im toward the end of the problem i just don't get the signs
 
hachi_roku said:
yes...like i said I've already worked that part...im toward the end of the problem i just don't get the signs

Well, since you have shown almost no work(step by step) it is hard to tell where you have missed, or what you are doing wrong.
 
got it...nvm..thanks
 
hachi_roku said:
got it...nvm..thanks

:cool:
 

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