How do I find the length of a curve using calculus?

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Discussion Overview

The discussion focuses on the method of finding the length of a curve using calculus, specifically addressing the integral formulation and the manipulation of differential elements involved in the process.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about how to bring out the dx in the integral for curve length, suggesting it may be an algebraic trick.
  • Another participant responds by stating that multiplying by dx/dx resolves the confusion.
  • A third participant corrects the integrand to include √(1+(dy/dx)²) for clarity in the context of the integral.
  • A later reply presents the expression [{1+(dy/dx)²}^0.5]dx as the length of the curve, reiterating the mathematical formulation.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the initial confusion regarding the manipulation of dx, although there is agreement on the correct form of the integrand for the length of the curve.

Contextual Notes

The discussion includes assumptions about the understanding of differential calculus and the specific context of curve length calculations, which may not be fully articulated by all participants.

derek181
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I am just learning how to find lengths of curves using calculus. √((dx)2+(dy)2)→∫√(1+(dy)2)dx. My question is how are you able to bring out the dx. Is this some sort of algebraic trick I've never heard of. Can someone please explain this to me?
 
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nevermind, you just multiply by dx/dx
 
You should have √(1+(dy/dx)²) for the second integrand.
 
It is [{1+(dy/dx)^2}^0.5]dx = Length of curve
 

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