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This video covers the basics of integral calculus, including how to calculate an integral and how to differentiate it. It also provides an example of how to apply integrals in a practical problem.

**00:00:00**In this video, a teacher presents the concept of integral and its usefulness. He explains that understanding the concept of integral is one of the magical pleasures life offers. The integral, often feared, is a mathematical tool that can be used to measure distances, but must be used cautiously as it can also be used to compare sizes. A square with sides of 1 meter is measured as 2 meters when it is compared to a unit of measure such as this paper square. Two squares with sides of 3 meters each are measured as 6 meters when compared to the unit of measure. The integral is a tool that can be used to measure dimensions in curved or non-linear ways. It was discovered by Archimedes over 2,000 years ago and he began to approximate the solution by placing squares that reached the curve to cover the entire surface. He then calculated the area of each square and added them all up to arrive at the area of the entire figure. This method became known as the "method of spheres." Archimedes realized that a more accurate way to measure surfaces would be to create more precise squares, and this is where the modern integral methodology began. Today's mathematicians are still trying to find a perfect mathematical formula to measure an object's area without having to measure its**00:05:00**The integral is a mathematical tool that was discovered by two brilliant minds, Newton and Leibniz, over 400 years ago. They both arrived at the same conclusion that rectangles cannot be used to measure areas with curved boundaries, so they developed a new method based on curves. This eventually led them to the famous formula for calculating the area of any surface, which they illustrated in a coordinate plane. They tested their theory by changing the curve to a straight line and seeing what area would remain under the function as x increased. They were able to find the approximate area of a figure by plotting points along the line and solving for x. This process can be repeated for any value of x. Thanks to these two pioneers, the integral has changed the course of modern mathematics and technology. In this video, I will review the steps that Newton and Leibniz took to arrive at their famous formula. I will also show you a simple function that allows you to visualize the area that is being calculated. Finally, I will demonstrate how to use this function to find the approximate area of a figure.**00:10:00**This video introduces the integral, which is a mathematical tool used to calculate areas under curves. It starts by explaining what an area is, and how to calculate it using basic algebra. It then moves on to discuss the integral, and its key properties. It provides a simple example to illustrate these concepts, and ends with a demonstration of how to apply the integral to a real-world problem.**00:15:00**The video discusses the importance of integral calculus, and presents a pedagogical approach for teaching it. It covers the basics of integral calculus, including the definition of an integral and its two main types - potential and real - and how to calculate them. It also explains how to differentiate an integral and how to find an integral of a function. Finally, the video provides an example of how to apply integrals in practical problems.**00:20:00**In this video, a teacher presents a method of calculating integrals that is based on the formula 4x cubo. This formula is known as the integral formula, and it is used to integrate a power, such as 4x cubo. The teacher also introduces the constant, 4, and demonstrates how to integrate the function 4x cubo given the equation x cuadrado. Finally, the teacher demonstrates how to calculate the area under a curve by using the integral formula.

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