Summary of Aplicaciones de la integral de Riemann | | UPV

00:00:00 - 00:05:00

This video discusses three applications of the integral of Riemann: finding derivatives of functions, calculating averages, and solving problems in which a function is defined at two different points. Martinez demonstrates how to apply these techniques using an example problem involving calculating the height of a rectangle with a base equal to the area of the graph of a function.

• 00:00:00 In this video, Maria Jose Martinez, a professor of mathematics at the University of Valencia, covers the basics of integral calculus, including the definition of an integral and the Riemann integral. The video then goes on to discuss three applications of integral calculus: finding derivatives of functions, calculating averages, and solving problems in which a function is defined at two different points. Martinez demonstrates how to apply these techniques using an example problem involving calculating the height of a rectangle with a base equal to the area of the graph of a function.
• 00:05:00 This video discusses applications of the integral of Riemann. First, we see that if the integral corresponds with a rectangle clearing m the average value of the function, this is this from here look at that this is an extension of the concept of arithmetic mean of a finite family of numbers applied to infinite values that a function has in an closed interval. For example, here you have the formula above to the right. We're going to calculate the average value of the function, x, by square root on the square, you have it in the graph in the interval 03 Pi if it's not that you need to review the formula identify the elements, we see that x is zero of stress pi and the integrating would be the function x by square of x square. Our integral is immediate and we get that the average value of the function in that interval is 0 0 185. The last application I wanted to talk about is limits and integrals. Some limits of sequences can be solved transforming into the limit of a verb that is a integral of this form. So you see here now. Then, later on, we'll explain the process of fixing your minds that for calculating a sum of the tree you need a partition of the interval considered here. You take a specific partition