Analytical Solution for the Perimeter of an Ellipse via a New Definite Integral: A Study on Elliptical Cylinder Sections

Research on the perimeter of an ellipse has so far only found approximations. This occurs because the integral of the perimeter of an ellipse does not have an antiderivative. Therefore, this study aims to find a new definite integral for the perimeter of an ellipse that has a derivative. This study observed the relationship between the intersection of an elliptical cylinder, which results in a circle, and the perimeter of the base of the elliptical cylinder. This study found a new definite integral to obtain the exact formula for the perimeter of an ellipse, which can be solved analytically.