What is integration? And what is derivation? And why are these important for us?
First, let’s discuss what integration actually is!
It is a process of assimilating different occurrences (variables). For example, if you are travelling from your house to your school in your car, its speed may vary, for some time you have to slow down your vehicle, some time you have speeded it up or there might come a time when you have to put a halt to it. If you were asked to tell at what speed (velocity) you have arrived at your school, you might not have an exact answer because the velocity kept changing with regard to time. To overcome these glitches, we use integration. We solve these small instances and then sum up all the variables and get the accurate value (velocity).
Integration helps the students to understand the problem deeply and minutely. By simply dividing the equation into smaller fragments, students can observe the minor details and by unraveling it, they can get an accurate answer.
Integration uses can be seen in many different domains like Electrical Engineering. Integration helps the electrical engineers to determine the exact place of; for instance; two substations so that there may not be any significant power or line losses.
Integration also plays part in Architectural engineering, it helps architectures to build the right infrastructure with minimal errors.
Integration helps Space Flight engineers as well, by determining the different space body velocities and hurdles they might experience when they plan longer missions to outer space.
Integration plays an important role in our everyday life. Students should be well aware of its uses as its uses can be seen in many other domains like Medical Sciences, Statistics, Research Analysis, Graphics and Chemistry. It increases the efficiency and enhances the productivity of finding the end result. It overcomes the surplus time or delays in solving any equation and prevents the excess use of resources. It gives us an ease in accessing variable data, resulting in better yield and stout progression.
Now, what is derivation?
Derivation is a word taken from derived, which means ‘to obtain’. In Mathematics, it means ‘to acquire’ something from another sequence by performing a series of operations.
Derivation of any function (variable) is the ability to change with respect to its argument (surroundings).
For example, if we have some money, we want to make profit with it. But we don’t actually know what will be the consequences of using it and where to spend it properly to get a desired profit. We will then check it; it will be like a sensitivity check more like a feasibility report. By making one variable constant (money), we can then check different variables (options) with it. At the end we can select the looked-for one.
Like integration, Derivation also has an imperative part in our daily lives. Its uses can be seen in businesses, where the businessman can determine the estimated profit and loss using the derivatives formulae.
Like mathematics, derivatives are used in physics too. It determines the efficacy of any vehicle by making a speed-time graph using derivatives.
Derivation has applications which determine the probability of earthquakes and has various uses in Seismology.
Regardless of any particular domain, it is essential to show pupils how different equations are formed so that they can understand the logic behind it and start reasoning with it. When students understand the reasons behind the problems, the problem-solving skills are ultimately developed.
In nutshell, integration and derivatives play a vital role in our daily life. It has its applications and uses seen almost in all domains whether in medical science or engineering. Students should explore these concepts to become a better spectator. Integration and derivation are top 2 concepts of math and students must learn how to calculate the equations. For practice students can use integration calculator and differentiation calculator online.