In Exercise 53 in Section 10.2 it was shown that the
Chapter 11, Problem 11.556(choose chapter or problem)
In Exercise 53 in Section 10.2 it was shown that the length of the ellipse , , where , is where is the eccentricity of the ellipse. Expand the integrand as a binomial series and use the result of Exercise 46 in Section 7.1 to express as a series in powers of the eccentricity up to the term in .
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