Determining the length of the curve (ln curve)

  • Thread starter Thread starter Riazy
  • Start date Start date
  • Tags Tags
    Curve Length
Click For Summary

Homework Help Overview

The discussion revolves around determining the length of a curve defined parametrically by the equations \( x = 1 + t + \frac{1}{t} \) and \( y = 3 - 2 \ln t \) for the interval \( 1 \leq t \leq 2 \). Participants are exploring the application of the arc length formula.

Discussion Character

  • Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the use of the arc length formula and attempt to set up the integral for calculation. There is a focus on ensuring the correct formulation of the integrand, particularly regarding the square root in the expression.

Discussion Status

The discussion is active, with participants clarifying the setup of the integral and addressing potential oversights in the formulation of the arc length expression. There is an acknowledgment of a mistake regarding the square root in the integrand.

Contextual Notes

There is a specific focus on the interval for \( t \) and the need to correctly apply the arc length formula, which may involve assumptions about the continuity and differentiability of the functions involved.

Riazy
Messages
30
Reaction score
0

Homework Statement



Determining the length of the curve (ln curve)
{ x = 1 + t + 1 / t
y = 3-2 lnt

between 1<= t <= 2

Homework Equations



Well Using the formula L = $ (from a to b) SQRT[x'(t)]^2 + [y'(t)]^2] dt

The Attempt at a Solution



I have a problem to go further from here, could someone help solve this?
 
Physics news on Phys.org
Using the formula you gave:

[tex] L=\int_{1}^{2}\left(1-\frac{1}{t^{2}}\right)^{2}+\left(-\frac{2}{t}\right)^{2}dt[/tex]

Expand and integrate...
 
hunt_mat:

I think you left out that the integrand in your expression for the arc length should be under a square root sign.
 
Your right, I have.
 

Similar threads

Replies
2
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 7 ·
Replies
7
Views
1K
Replies
7
Views
3K
Replies
5
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K