How do you find the arc length of the curve #y= ln(sin(x)+2)# over the interval [1,5]?
You'll need numerical methods.
Note that for
You need to find
I can't find a closed form antiderivative (Wolfram Alpha gives one that uses elliptic integrals of the first and third kind. http://www.wolframalpha.com/input/?i=int++sqrt%281%2B%28cosx%2F%28sinx%2B2%29%29%5E2%29+dx )
Use your favorite approximation technique to get an answer close to 4.23701 (also from WolframAlpha).