I'm currently trying to find the length along function of ln(x) for the heck of it.(adsbygoogle = window.adsbygoogle || []).push({});

I set up this integral for length

L= int/ sqrt(1+(y')^2)

so y'=1/x

so the integral becomes

int/ sqrt(1+(1/x^2)) = int/ sqrt(x^2+1)/x

So I used trig substitution. I set

tanA=x

secA=sqrt(x^2+1)

dx = sec^2(A) dA

so the integral becomes

int/ secA/tanA * sec^2A dA= int/ sec^2A cscA dA

d/dA cscA = -cotAcscA rearrange this and get -dsecA = cscA

so the integral becomes - int/ sec^2A dsecA

set u=secA

so the integral becomes - int/ u^2 du

so -(u^3/3) evaluated from limit a to b

let the original limits be x=1 and x=5

therefore they become A=arctan1 and A=arctan5

and u=sec(arctan(1)) and u=sec(arctan(5))

where sec(arctan(1))=sqrt(2) and sec(arctan(5)=sqrt(26)

However, if you plug these limits in you get a negative answer. Where did I go wrong?

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# Homework Help: Finding length along ln(x)

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