Definite Integral

Definite Integral

1. problems expressed by integrals

   • Area down the curve
     • The formulation of the area under a curve is the first step to develop the concept of integral. The area under the curve formed by the trace of the function f (x) and the x axis can be obtained approximately, by drawing rectangles of finite width and height f equal to the value of the function in the center of the interval.
   • Moments of inertia of flat bodies
     • The moment of inertia of an object depends on its mass and the distance from the mass to the axis of rotation. This moment is not a single fixed amount, since if the object is rotated around a different axis, it will have a different moment of inertia, since the distribution of its mass in relation to the new axis is normally different. To change the rotation speed of an object with a high moment of inertia, a greater force is needed than if the object has a low moment of inertia.
   • Length of curves
     • Arc length, also called rectification of a curve, is the measure of the distance or path traveled along a linear curve or dimension.
   • Centroids of flat figures
     • is the coordinate of a point that belongs to a figure. Like the center, the centroid has coordinates according to the position it occupies in space. There are centroids of line, area and volume. In this part of the mechanics we will analyze the centroids of area and we will study the plane figures.
   • Solids of revolution
     • It is called solid of revolution or volume of revolution, the solid obtained by rotating a region of the plane around a line located in it, which may or may not cross. This line is called the axis of revolution. Let f be a continuous and positive function in the interval [a, b].