Finding the Length of a Curve: Step-by-Step Guide

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    Curve Lenght
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Homework Help Overview

The discussion revolves around finding the length of a parameterized curve defined by the equations x = sqrt(5)sin(2t) - 2 and y = sqrt(5)cos(2t) - sqrt(3). Participants are exploring the steps necessary to approach this problem.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need for the arc length formula for parameterized curves and question the specific interval for the parameter t over which to compute the length. There is also mention of the integral involved in the calculation.

Discussion Status

The discussion is ongoing, with participants providing hints about the arc length formula and the importance of defining the limits for t. There is no explicit consensus yet, but guidance has been offered regarding the integral setup.

Contextual Notes

There is a noted requirement to specify distinct values of t for the computation, which may influence the approach to solving the problem.

mugzieee
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i got a problem that says:
x=sqrt(5)sin2t -2
y=sqrt(5)cos2t - sqrt(3)

how would i go about starting it?
 
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Do you know the equation for arc length for a parameterized curve?

--J
 
One other thing:You may want to know between which points you wish to compute the length...?In other words,give 2 distinct values of "t"...The integral doesn't seem to be difficult...

Daniel.
 
mugzieee said:
i got a problem that says:
x=sqrt(5)sin2t -2
y=sqrt(5)cos2t - sqrt(3)

how would i go about starting it?
[tex]:(1): \ \ \ \ (CurveLength_{t=a}^{t=b}) = \int_{a}^{b} \sqrt { (\frac {dy} {dt})^2 + (\frac {dx} {dt})^2} \ \ dt[/tex]

(HINT: If solved correctly, this problem simplifies very rapidly!)


~~
 

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