Abstract
Integral can be used to determine several quantities, one of them is to determine the length of a curve in the plane. It can be applied to prove the circumference formula of a circle. This research aims to explain how to prove the circumference formula of a circle using a single integral expressed in both cartesian and polar coordinates. The method used in this research is a study of literature. The result of this research shows that proving the circumference of a circle can be done by determining the implicit derivative of the circle equation. Then, the circle equation and its implicit derivative are substituted into the integral formula for determining the length of the curve in both cartesian and polar coordinates so that the circumference formula of a circle is obtained.
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