Indefinite Integration for JEE Maths

In this particular blog, we’ll be discussing one of the topics which are considered very hard to study in the syllabus for JEE Maths. Hopefully, this article can clear your doubts and shed some light on how to best prepare for indefinite integration from study materials like NCERT and JEE Main answer key. As long as you are not afraid of the topic and willing to learn, you can understand it very well. So now, let’s get into the topic of indefinite integration for JEE Maths.

The Concept of Integration

In the simplest of terms, integration refers to adding up or combining two or more things (addition). However, this form of addition is done on infinitesimally small intervals (pretty much zero). In mathematics, it is also called the reverse process of differentiation. This type of integration is done without any upper and lower limits, and thus, it is called indefinite integration.

Where C represents the integration constant which would not be present in case of definite integration.

For JEE

The formula for integration can usually be proved as the anti-derivative.

Thus, by definition

So similarly, others also follow and you can locate them easily in any CBSE or JEE main Maths preparation textbooks. However, the best books I would suggest are NCERT mathematics part one and two. Here, are given some important special integrals which you must remember while solving the JEE Math problems.

Now, let’s get to the main aspect of JEE Integration. That questions that are asked usually come in the form of the three following categories.

The Powered Problems

In order to solve this problem, the first thing that you have to do is to take the highest power of x (in this case 4) outside. The problem is constructed in such a way that the differential term inside the bracket will be 1 + (1/x4), which is exactly equal to the value outside the bracket 1/x5

The Substitution Problems

In the case of substitution problems, you have to try to eliminate by substituting x with asin2/3 θ, and so a gets cancelled out from both numerator and denominator. Then the problem becomes an easy one. Try to substitute x with tan θ. If there is only 1 + x4 in the denominator then consider dividing numerator and denominator by x2 terms and proceed by method 1.

The Recursive Problems

You have to understand this topic very well, as this is the most frequently asked topic from the subject of indefinite integration in JEE Maths. So what does recursion mean?

In the recursive approach, you have to find out what is:

This is an interesting approach. Let’s check out the following.

Or,

Thus, we have successfully arrived at our recurrence relation. If we know I0, we can find I2 and then I4 and hence all the values that n can take.

Best Books for Indefinite Integration JEE

We have since already discussed important problems on the subject of JEE integrations, let’s take a look at all the necessary study you will need to score the best in your JEE mains and Advanced. These books will very much come in handy for you and help you strengthen your skills for JEE integration. The following books are listed in accordance with their importance, chronologically.

NCERT

NCERT is the most fundamental and basic reference material for any student preparing for JEE Mains and Advanced. NCERT is used by schools as their official syllabus and many coaching institutions use this as well. It can clear all your basics and help you understand all concepts in an easy manner.

Cengage Calculus

This book has many, many solved examples on the topic of indefinite integration and will give you a good idea on how to solve this topic’s problems. The level of problems in this book range from very difficult to very easy. You shouldn’t waste much of your time working the easy problems, they are hardly ever asked in the syllabus. They are there to give you an idea of the subject. So focus your attention on the more difficult questions which will be a far better help during the actual exam. The book has all the questions clearly explained and answered, better than you can find in any coaching class.

Integral Calculus by Amit M. Agrawal

This is one the best but also very complex books on indefinite integration. However, it is considered the best book for JEE preparation. There are some questions in this book which are even above the level of JEE students. Whereas, the majority of questions are perfect for JEE. The book starts out by discussing all the methods of integration, which is followed by multiple examples to help explain the concept better. The recursion concept is explained very well in this book. You must remember to study recursion well. All the questions have solved answers or answer keys to make them easy to understand.

Coaching Material and JEE Main Answer Key

Don’t forget to through coaching materials of various institutions. They have some of the most thoroughly explained theories and solved problems because remember, the more problems you solve the better your chances of clearing JEE. Also, refer to previous years’ JEE Main answer key.  JEE Main Answer Keys are a vital tool for getting a good understanding of the paper pattern. And the type of questions that will be asked related to Indefinite Integration.

Finally, some general tips on how best prepare for your mains and advanced.

You should find out which subjects have a higher weightage in terms of marks and should focus on perfecting them. Moreover, this will improve your chances of scoring higher. Your time management must be impeccable. Split your whole syllabus over a period of months and study a couple of topics each day, but in depth.

I feel this is the biggest problem. Keep next day planned before going to bed and set goals for the week. You may include hourly deadlines for homework, revision, breaks, exam dates and weekly targets. A healthy diet always helps to keep the mind focused and sharp. Revise each topic multiple, especially topics you are good at as they’ll score you the best marks.

And finally, when giving your exam, stay calm think logically, focus first on questions you are good at and do not panic.