I'm on exam 4, question 5 b) and asked to set-up 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/18-01sc-single-variable-calculus-fall-2010/unit-4-techniques-of-integration/exam-4/session-86-materials-for-exam-4/MIT18_01SCF10_exam4sol.pdf
OCW Scholar - Single Variable Calculus
Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
I 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!
*x was given as a function of y
The initial condition is implicit in the choice t=y. We could have made the choice s=y-1, 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.