Circumference of a circle in parametrics

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Homework Help Overview

The discussion revolves around finding the circumference of a circle defined by the equation x² + y² = 1, specifically through parametric equations and conventional integration methods. Participants are exploring the implications of singularities in their calculations and the necessity of different approaches to arrive at the correct answer.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss isolating y and finding dy/dx, as well as the use of integrals to compute the length of the curve. There are questions about the validity of using parametric equations versus traditional methods, and the need to address undefined values in the integrals.

Discussion Status

Some participants suggest using trigonometric substitution to handle singularities in the integral, while others express a desire to resolve the problem using both parametric and conventional methods as required by their instructor. There is an acknowledgment that the parametrization may only cover half the circle.

Contextual Notes

Participants note that the teacher has requested solutions using both parametric and conventional methods, which adds constraints to their approaches. The discussion also highlights concerns about undefined values at specific points in the integration process.

hangainlover
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Homework Statement



x^2+y^2=1

Homework Equations



length of curve square root (1+(dx/dy)^2)dy or square root ((dx/dt)^2 + (dy/dt)^2) dt




3. The Attempt at a Solution [/b

I isolated y and got y= square root (1-x^2)

finding dy/dx = -x/square root (1-x^2)
i plugged that into the formula but i did not get the correct answer.

im aware that if i do integral of square root (1+ (dy/dx)^2 ) i have to do imporper integral as i get undefined for denominator at x=-1,1 so what should i do
we all know that answer should be 2pi
 
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Ignore the 'undefined' issue. Just do a trig substitution to solve the integral. Once you've done the trig substitution you won't see the singularity. BTW you'll get pi, not 2*pi. Your parametrization only covers half the circle.
 
I know, i can get the answer by defining the circle in trig.

But, shouldn't i be able to do it in conventional way and by paramatrization as well?
i just need to take care of the x values and t values where the function gets undefined.
My teacher wants me to do it in these two ways.
 
Even to do it in the x-y way you need to integrate 1/sqrt(1-x^2) from -1 to 1, right? Even if you haven't parametrized it as a trig function you still need to do a trig substitution to solve that integral. That's what I'm talking about.
 

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