Curvas planas parametrizadas

Abstract

In the study of Cartesian curves we are accustomed to taking a variable as independent and the other as dependent, ie y = f(x) or x = h(y). However, some movements or paths are inconvenient, difficult or impossible to describe by a function of a variable or formula of the form y = f(x). Instead of defining y in terms of x or x in terms of y define both x and y in terms of a third variable called parameter. Such curves parameters are called parametrized curves. In this work we present techniques to sketch such curves, we find parametrizations for some classical flat curves and also did a study on the length arch areas, curved boundary areas, and surface areas of revolution.