Length of Sine Curve

1. Apr 15, 2012

I tried to find the length of a sine curve using calculus.I got stuck in the integral of integral(sqrt(cos(x)^2+1), x, 0, a). Limits are from 0 to point a,i.e. length of curve from 0 to any point a.With some approximations I found out the length of sine curve as a result.I have attached the derivation of my result.I tried searching books and internet for this result.But couldn't find like this one.It also seems that this result gives more precise answer.

Attached Files:

• Attempt to find length of sine curve from 0 to any a.pdf
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2. Apr 15, 2012

chiro

3. Apr 16, 2012

I know elliptic integrals.It comes when you try to find time period of a simple pendulum without taking usual approximation:that angular displacement is very small and that
sin(θ)≈θ in radians.But even elliptical integrals can't be solved analytically.You have to solve it in a calculator/computer or use interpolation formula's to carry out integral approximately.However the method of approximation which I used gives a result which gives better answer compared to a calculator or interpolation.In the end of pdf I have given three checks of that result which I haven't seen anywhere.I have also searched the net extensively.That's why I posted here to ask you guys if it's a new result or not??

4. Apr 16, 2012

chiro

I don't know if its a new result or not (hell I didn't know what an elliptic integral was!). Hopefully somebody else can give you a better answer.

5. Apr 16, 2012