Integrali - Introduzione | Andrea il Matematico

Hello everyone! Have you ever wondered what an integral is? In this video, we'll look at the definition to clarify this aspect and provide a mathematical definition of an integral. Before answering this question, I'll ask you a question that will help you understand the concept of an integral. Suppose you're an engineer and need to calculate the area of ​​an irregular piece of land. Now, from your school experience, you probably know how to calculate the area of ​​a rectangle (using the base times the height). But how can you calculate the area of ​​an irregular shape? A difficult question, I see. You could imagine dividing the land in question into many small rectangles (or squares, if you prefer) and adding all their areas together. Obviously, the area won't be precise, only approximate. You'll surely notice that the smaller the rectangles, the more precise the area will be. This is exactly what integrals are for! Adding many small pieces together to calculate a total area. The integrals we will describe in the video are associated with the equation of a function. From a historical perspective, the concept of integrals is linked to the calculation of space. Knowing that velocity is the ratio of space to time, space can be viewed as the product of time and velocity. Now imagine that velocity undergoes continuous changes over time. To calculate the total distance traveled, we could add many small pieces of space. Each piece of space will be the product of the velocity at a given instant of time and that instant of time itself. Now let's move on to the content of our lesson. An integral can be understood as the area between the function and the x-axis, bounded by two values ​​of the x-coordinates. During the lesson, we will revisit the fundamental reasoning that will lead us to calculate this area as the sum of the areas of very small rectangles. The integral will therefore be defined as a sum of infinite areas of very small rectangles. The elongated S, symbol of the integral, identifies this very long sum. 👍🏼Leave a LIKE if you found the video helpful! ➡️Next lesson on integrals:    • Integrali - Integrale Indefinito e Funzion...   🔁Video playlist on integrals:    • ✍🏻INTEGRALI   To discover all my courses, you can visit my website here: https://andreailmatematico.it/ ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ Subscribe to my channel here:    / andreailmatematico   Visit my website: https://andreailmatematico.it/ Follow me on Facebook:   / lamatematicadiandreailmatematico