With the help of integral, we can describe the movement of different objects. For example, by having the graph of changes in the speed of the object in terms of time, we can easily obtain the distance traveled by the object in a certain period of time. Finding the probability of random and continuous variables is another important application of integral. Continuous random variables, such as temperature, can have any value. We can use this feature to solve many statistical and probability problems.
In physics, the integral is used in many fields. For example, we use integral in calculating the center of mass and center of gravity of complex objects such as cars and buildings and in order to optimize stability and weight distribution. Also, the integral has an important application in fluid mechanics to calculate the flow, pressure and volume of liquids.
The integral also plays a very important role in the development of computer science. Integral helps us to measure and analyze continuous and gradual changes in various systems. As a result, this ability has made the integral a powerful tool in various areas of computing.
With the help of integral, we can describe the movement of different objects
Image processing is one of the most important integral applications. Suppose we are looking to detect the edges of an image or some of its special features, with the help of integral we can measure the changes in light intensity at different points of the image and identify the edges. This helps the computer to better understand different images.
In computer graphics, with the help of integral we can create three-dimensional images and realistic effects. For example, to calculate the light and shadows in a 3D scene, we need to calculate the integral on different surfaces. Also, in machine learning, integral plays an important role in optimizing models and learning from data. Many machine learning algorithms work based on the calculation of integrals. For example, in neural networks, the integral is used to calculate the error and optimize the weights of the network.
Amazing applications of differential equations in everyday life
So far, we have talked about the applications of derivative and integral separately in different fields, but we must know that these two topics are not separate from each other and are closely related to each other. We can see this close relationship in differential equations and their solutions. With the help of these equations, we can understand how nature works.
Differential equations are a complex topic in mathematics, and we cannot easily solve all the resulting equations, but at least we get some interesting information from them. For example, we use differential equations to obtain a model for population growth, fluid movement, describing the movement of an object after a certain force is applied to it, and the behavior of electromagnetic waves.
With the help of differential equations, we can understand how nature works
Even to describe the movement of satellites that move around the earth or rockets that we launch into space, we should not neglect the vital role of differential equations. Similar to the simple algebraic equations that we learned in high school, differential equations have their own unique meaning and story. To solve these equations, we use integral and derivative at the same time.
Now let’s go into details and after examining an example of the application of differential equations in real life, we will examine the application of these equations when launching a rocket into space and its movement in space.
You probably watched the series Numb3rs between 2005 and 2010. In one of the scenes of the series, the law enforcer is looking for a couple who have committed several crimes while traveling around America. The FBI is following the couple’s movements on the map, but they have not been able to arrest them yet. In the continuation of the series, mathematicians try to predict their destination by examining the path taken by the criminal couple with the help of a curve called “Pursuit Curve”.
