Formulas For Calculating The Areas Of Regiones Bounded By The Quadratic Function And The Line, Two Quadratic Functions

Abstrak

This article brings formulas for finding the areas of regiones bounded by the quadratic function and the x-axis, the quadratic function and the line y=kx+l , two quadratic functions and they are generalized. The generated formulas can be used in problems concerning the calculation of the area of the region bounded by the quadratic equation in the definite integral. In the secondary schools mathematics course, the define integral topic presents problems of the quadratic function concerning with the area. The article is viewed for the general equation of the quadratic function and induced a formula related to the discriminant, roots and prime coefficient of the quadratic polinomial. Vieta’s theorem was used to create formulas. From the geometric point of view,  the area bounded by the x-axis and the quadratic function equal to 2/3  part of the rectangle, which sides equal to the subtraction of quadratic polinomial roots and ordinate of vertex of a quadratic function (parabola). In conclusion formula 2 is induced. Since the area of the region is a positive, its absolute value is used in the formula.