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katzndogs
 3 years ago
I'm on exam 4, question 5 b) and asked to setup an integral for arclength along a curve. I don't understand how the answer parametrizes the curve though without any initial conditions, here's the link:
http://ocw.mit.edu/courses/mathematics/1801scsinglevariablecalculusfall2010/unit4techniquesofintegration/exam4/session86materialsforexam4/MIT18_01SCF10_exam4sol.pdf
katzndogs
 3 years ago
I'm on exam 4, question 5 b) and asked to setup an integral for arclength along a curve. I don't understand how the answer parametrizes the curve though without any initial conditions, here's the link: http://ocw.mit.edu/courses/mathematics/1801scsinglevariablecalculusfall2010/unit4techniquesofintegration/exam4/session86materialsforexam4/MIT18_01SCF10_exam4sol.pdf

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katzndogs
 3 years ago
Best ResponseYou've already chosen the best response.0I instead found arclength in with respect to y since the x was given as a function of x but I m sure looking through my notes there whenever asked to parametrize initial conditions for t were provided. So any one out there with any idea could you be so kind to help. Thankyou!

katzndogs
 3 years ago
Best ResponseYou've already chosen the best response.0*x was given as a function of y

beginnersmind
 3 years ago
Best ResponseYou've already chosen the best response.1The initial condition is implicit in the choice t=y. We could have made the choice s=y1, which would have given x=s+1+(s+1)^3. We would need to change the limits of integration s=0 and s=3 (the values corresponding to y=1 and y=4). So we would integrate a slightly different function over different limits, leading to the same arc length. It's a matter of choice and if you try anything else you'll see how t=y leads to the simplest result.

katzndogs
 3 years ago
Best ResponseYou've already chosen the best response.0I understand now! Thanks so much man for that great explanation! :)
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