The changing rate of a function is known as a derivative.
These functions act to the real numbers.
The alternative term of derivation is integration. The process of finding integrals is integration. Integrals have been used to find many useful measures such as volumes, area, displacement, and many more.
Derivative and integration are an inverse function of each other. These are inversive in the way that derivatives find slopes and integration find volumes, areas, etc.
The area is a product of a and b and the slope is a ratio of y/x. And, this division and multiplication are an inverse function of each other.
Why derivatives and integration are beneficial?
Derivatives and integration have been used for understanding the basics of other subjects such as Physics, history, and economics. For example, acceleration and speed are terms of physics.
These two terms are required to find these terms. Derivatives also help in finding the growth rate. Derivative calculator makes it easy to get quick results.
Applications of derivatives and integration:
Application of derivative:
1: To find the minimum and maximum values of functions
2: Helps to model the objects in motion
3: Used to measure the air pressure
4: To measure the change rate
5: To draw complex curves and graphs
Applications of integration:
1: To determine the under curve area
2: To determine the angles between curves
4: Used to calculate the work done of a variable force
5: Used in history, economics, mathematics, and geography.
Undergraduate students face difficulty to solve derivative and integration problems. A study has been conducted to find why students feel difficulty in learning derivative and integration. The result of this study showed that these difficulties include weakness to recall previous knowledge, connection weakness between the symbolic and embodied mathematical world, and problem-solving inability. To solve equations quickly once can use an integral calculator as well.
Moreover, this difficulty is also because of insufficient practice and geometrical intuition. It’s also because of insufficient knowledge of functions.
Is integration more problematic than differentiation?
Some studies showed that integration is more problematic than differentiation.
From a symbolic computational viewpoint, integration is more severe than differentiation.
Solving differential equations is always possible. Integration is not possible in many cases.
Consider an example.
Let suppose a question of differentiation and integration has been given.
You’ll get a simple expression after applying the chain rule, quotient rule, or product rule. On the other hand, you have to match the templates in case of integration. It is the reason that makes differentiation easier than integration. Also, it is a personal thing. Some people find differentiation difficult.
But some consider that integration problematic. It depends on the student which term he understands faster.
How to remove difficulties in solving derivatives and integration?
Calculus is an important subject. You’ll get command over calculus if you put effort into it.
The practice is the easiest way to get mastery. Try to get a problem relatable to your daily life and then find a solution according to this image. In this way, things will become relatable.
Before solving the questions, you must understand its basics. It is because poor knowledge will only enhance your problems.
Firstly, you need to be familiar with derivatives. You should understand the concept of derivatives properly then come towards integration.
Understanding of differential makes the integration easy to understand. Moreover, practice problems, tutorials are an excellent source for understanding this concept.
Try to solve problems in your mind also. Also, one of the efficient ways is to solve a lot of
problems. It is because math is a subject of practice. Try to solve the problems step by step.