How to Evaluate an Integral | The Easiest Way Possible

How to Evaluate an Integral

Mathematics was a nightmare for almost half of the student population. Understanding those theorems, formulas, tricks, properties, evaluate an integral etc. always scares the hell out of them. As time passed, the two biggest fears came, and they were Integration and Differentiation. Understanding them and solving them was only a task of a pro.

Evaluating an integral is very simple and uncomplicated if done with proper attention and understanding. Mastering the art of Mathematics can be tricky, but when someone grasps; it can turn out to be the best part.

See: Trigonometric Integrals Explained [What are Trigonometric Integrals?]

Integration is a very decisive and crucial part of a mathematician. It requires many properties, formulas, tips, and tricks to be simplified easily.

If you want to become an expert in solving integrals, then it will be your first stop. Here, we will teach you some tricks and tips for easy learning and expertise. The foremost key to becoming successful is to remember that the more you practice, the more you learn.

What Are Integrals?

Integrals are the opposite of derivatives. These are mathematical objects that; assigns on functions such that they can describe an area, displacement, volume, and many other things. Since they are the opposite of derivatives, they are also known as anti-derivatives.

Do’s And Don’ts

To evaluate an integral it can be tiresome if not done with interest and enthusiasm. But for getting the best output, a little poise and care are necessary. Every single condition has to be taken care of for getting the perfect solution.


  • Learn all the properties.
  • Keep in mind all the formulas.
  • Always use hit and trial methods.
  • Solve more and more examples.
  • Follow every single step for solving.
  • First, understand the problem and then solve it.


  • Never run to get the solution. Always give your time to the query.
  • Do not hesitate to ask the queries.

How To Evaluate An Integral Properly

To evaluate an integral properly, one must completely be aware of all the formulas, properties, and methodologies. Knowledge about the right data will thoroughly help you in achieving success. Follow every single step given below for mastering the art of integration.

Explore More!

The more you explore, the more expert you become. If you want to learn to evaluate an integrate properly, then you should try to gather data from various sources like different books, YouTube, etc. Find different tutorials from YouTube and try to grasp enough knowledge from them. Solve different questions as much as possible.

Solving examples are the best help over here. You can easily detect your errors if trying to solve a previously done query. Read various books for more tips and tricks for easy simplifying. Learn the basics well. Learning basics is the first step of the ladder to become a pro to evaluate an integral properly.

Properties To Remember

For solving an integral it is very important to keep in mind all the properties which associates with it. These properties enable us to simplify the problem easily. The properties are simple to lean if you practice for it daily.

  • ∫ab f(x) dx = ∫ab f(t) dt
  • ∫ab f(x) dx = – ∫ba f(x) dx … [Also, ∫aa f(x) dx = 0]
  • ∫ab f(x) dx = ∫ac f(x) dx + ∫cb f(x) dx
  • ∫ab f(x) dx = ∫ab f(a + b – x) dx
  • ∫0a f(x) dx = ∫0a f(a – x) dx
  • ∫02a f(x) dx = ∫0a f(x) dx + ∫0a f(2a – x) dx
  • Two parts
    • ∫02a f(x) dx = 2 ∫0a f(x) dx … if f(2a – x) = f(x).
    • ∫02a f(x) dx = 0 … if f(2a – x) = – f(x)
  • Two parts
    • ∫-aa f(x) dx = 2 ∫0a f(x) dx … if f(- x) = f(x) (if even function)
    • ∫-aa f(x) dx = 0 … if f(- x) = – f(x) (if odd function)

Step By Step Evaluation

Follow every single step for getting the correct output. Missing out on even one step can make your entire effort worthless. To evaluate an integral, you need to follow a well-maintained procedure. Read and study the process from various books and guides and try to solve the questions by yourself.

Do not rush into getting an answer. Be calm and patient and follow each step as mentioned in the guides. Even if it takes a lot of time for solving the query, never lose your patience, and achieve your goal. After some time it will be a left-hand play for you to solve integrals.

Clear Your Doubts

Never hesitate to Ask! If you are not clear with even a single little point, do not keep the doubt to yourself. Take guidance from a person who can help you in clearing your doubts. Small mistakes can lead to big troubles.

Avoiding silly mistakes can be a considerable hindrance in problem-solving. You may also end up wasting your time and getting no proper solution. Even if you think, it is a very minute mistake to ask about, reach out to someone who can help you in understanding the problem.

All Set To Go!

Mathematics can turn out to be the best and the most fascinating subject if studied with full dedication and enthusiasm. Integrals being a part of it are also very simple to evaluate if all the above tips are followed properly. One must have to get the proper guidance before beginning.

Refer: What are Improper Integrals? [Explained Easily with Examples]

Always remember the most crucial key to success is practice. Solving more and more examples, practicing more and more questions and learning new tricks and techniques can guide you all the way how to evaluate an integral.


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