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Algebra |
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Authors: Tai-Choon Yoon
Int(f(x)^2+g(x)^2)^(1/2)dx and Int((dx/dt)^2+(dy/dt)^2)^(1/2)dt are integral equations that appear in the process of calculating the length of an ellipse. They do not provide an exact solution, and already known solutions are somewhat complicated. The solutions both the two elliptic integral equations above can be obtained by the method of eliminating the square root. The arc length of an ellipse is given by l = aθE(k), and E(k) is expressed as a power series regarding the eccentricity of the ellipse.
Comments: 5 Pages.
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[v1] 2024-12-12 11:12:13
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