Arc Length (Set up the Integral)

Click For Summary
SUMMARY

The discussion centers on calculating the arc length of a parametric curve defined by the equations x = t + cot(t) and y = t - sin(t) over the interval 0 ≤ t ≤ 2π. The correct formula for arc length involves evaluating the integral 2π ∫sqrt(3 - 2*sin(t) - 2*cos(t)) dt from 0 to 2π. A participant initially expressed confusion but later clarified that the arc length should be computed using the formula sqrt[(x')^2 + (y')^2], which is essential for solving such problems.

PREREQUISITES
  • Understanding of parametric equations
  • Knowledge of calculus, specifically integration techniques
  • Familiarity with derivatives and their applications in arc length calculations
  • Basic trigonometric identities and their derivatives
NEXT STEPS
  • Study the derivation of the arc length formula for parametric curves
  • Practice evaluating integrals involving square roots and trigonometric functions
  • Learn about the properties of cotangent and sine functions in calculus
  • Explore examples of arc length calculations in different contexts
USEFUL FOR

Students and educators in calculus, mathematicians focusing on parametric equations, and anyone seeking to deepen their understanding of arc length computations in mathematical analysis.

johnhuntsman
Messages
76
Reaction score
0
x = t + cot t
y = t - sin t
0 ≤ t ≤ 2π

Somehow the answer is:


∫sqrt(3 - 2*sin t - 2*cos t) dt
0

I'm afraid I don't know where to start on this one. I don't need someone to walk me through it (probably) but a point in the right direction would be appreciated.
 
Physics news on Phys.org
Nevermind this post everyone. I made a foolish mistake. I'm supposed to do sqrt[(x')^2 + (y')^2] for anyone who makes the same mistake and comes across this in a Google search. It was in an earlie rpart of the chapter I'm working on even. Sorry everyone.
 

Similar threads

Replies
2
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 7 ·
Replies
7
Views
1K
  • · Replies 9 ·
Replies
9
Views
1K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K