(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The task is to solve for the arc length of an ellipse numerically. a & b are given for an ellipse centered at the origin and a value for x is given.

2. Relevant equations

Equation of ellipse is given to be

[tex]x^{2}/a^{2} + y^{2}/b^{2} = 1[/tex]

and the equation to solve for the arc length is given as

[tex]a \int^{\theta}_{0}\sqrt{1-k^{2} sin^{2}t} dt[/tex]

Assuming a is the major axis

3. The attempt at a solution

The additional condition is that

[tex]-a \leq x\leq a[/tex], so [tex]\theta[/tex] can be [tex]\ge 0.5 \pi[/tex]

Since [tex]\int^{\theta}_{0}\sqrt{1-k^{2} sin^{2}t} dt[/tex] does not seem to work when [tex]{\theta} \ge 0.5 \pi[/tex]

The only solution I can think of is as follows

- If x < 0
- pb4 = quarter the perimeter of the ellipse
- Set x= -x (reflect about the x axis)
- ptemp = arc length for the positive x
- The final answer would be p=pb4+(pb4-ptemp)

This would mean evaluating equation [tex]\int^{\theta}_{0}\sqrt{1-k^{2} sin^{2}t} dt[/tex] twice.

Is there a better solution to this problem?

Thanks,

- Sid

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# Homework Help: Solving for arc length of an ellipse

Can you offer guidance or do you also need help?

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