Reasons Why Should Students Give More Emphasis on Derivatives and Integrals

No wonder in saying that all students are not supposed to welcome the subject of Math with open arms. Additionally, when it comes to Calculus, the reasons for a nightmare for many would-be, Derivatives, and Integrals. Let narrow down the question of why students should give more emphasis on Derivatives and Integrals.

Why should students emphasize on Derivatives?

A central issue is how derivative is taught prior to Integrals. The heart of the problem is that students are only left with the idea of an instantaneous rate of change when they ask about Derivation.

Primarily, it is true that derivatives tell us about the rate of change, i.e., delta. But does it justify the significance of derivatives for students? 

The student should emphasize derivative because it tells us where the best place to sit is, in case the room is filled with smoke.

Similarly, these optimization models of derivation also help us in improving decision making in healthcare. Derivation helps students understand that acceleration is the derivative of speed. In the last centuries, manufacturers have worked a lot on it, ranging from cars to rockets.  

To grasp the problems of derivatives entirely, one should make outlines in the form of an algorithm. The algorithm will lead students to explore the working of derivatives with more eloquence.

Have you ever got a penalty ticket for over-speeding? If yes, the reason was your derivative was higher than legally allowed. Speedometer, which displays the speed of your vehicle at a particular instant, uses the concept of calculus.

When the rate of change of speed with respect to time is as small, so negligible that it can be regarded as 0.

Moreover, the derivative calculators are used in finding the rate of change, the slope of the tangent, marginal profit, marginal cost, marginal revenue, linear approximations, infinite series representation of functions, optimization problems.

Learning by textbook is sometimes a difficult task so lots of teachers are recommending students to use calculators and converters more frequently.

I wished I had both while I was studying! Calculators and Teachers 

Why should students emphasize on Integrals?

The reason for emphasizing Integration is simple and obvious because it's a generic way of adding slices to find the whole.

While practicing integrals on paper, you are basically adding up the area of each of those rectangles to find an approximation of the area under the curve. You can have an idea by looking at the picture below,

Integrals can be used for computing the area of a two-dimensional region that has a curved boundary, as well as computing the volume of a three-dimensional object that has a curved boundary.

The area of a triangle is different from the formula of the area of a trapezoid and spherical curves. Hence, integration deals with them all in one single umbrella of its calculations.  

Just as the process of differentiation is used to find the slope at any point on the graph, the process of integration finds the area of the curve up to any point on the graph.

Thus, we can say that the integral comes from not only trying to prove the inverse process of taking the derivatives but mainly trying to solve the area problems.

As due to its property of dealing with the area under curves on the graph, we can find numerous values of real-world phenomena by merely putting the coordinates of the graph.

For example, the student should also emphasize integrals because it can help them to find work done on a particular object. The work, which is the area under the curve, always depends on the force and the displacement of the moving object.

Therefore, finding the area under the curve will easily give you the work. There are many online integral calculators available for quick and accurate calculations.

 As discussed above, you can also use the triangle equation, which will give the same amount of work, but integral will save you from memorizing or rote elementary algebraic formulas.

This is the reason which distinguishes integrals and makes it the primary choice.

Wrapping Up

Calculus is one of the main subject within mathematics. There are so many applications of calculations we come across in our routine life.

There are different ways that make you find step by step results and do practice but these means are not for students. Some developers and companies have invested in python and other open source programs and providing quick and useful material for learning and practice.

I found derivative calculator and integral calculator so much useful. These websites are providing step by step results for free without any subscription.

There are other websites that are also providing step by step results but they are not doing it for free.

As we are progressing more I think calculators will become more common to use. There are still some teachers that are hesitant while allowing their students to use them.

Their concern is right because you don't know whether a online tool is providing you correct answer.

But for students, it is essential to learn these ideas. Calculators can speed up this learning by doing practice on run time. But, it is not the only way of learning.

Students can still stick with traditional way of learning or whatever suits them.