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Practise solving tricky integration problems for JEE MAIN and JEE ADVANCED

Updated on October 4, 2014

Importance of solving tricky integration problems for JEE MAIN and JEE ADVANCED

If you scrutiny previous years' IITJEE papers you will observe that integration problems have been given considerable importance in these papers. Moreover, these problems are of such wide variety that they may baffle you at the exam if you are not well prepared for them. To be able to solve them fast, as is required at the level of IITJEE type exams, you will do well to practise:

1. Guessing the type of solution for a given integration problem, and

2. Memorizing all the formulae required to carry out such integration problems.

Following problems are given for your practice. First try to solve them yourself and in case you find them difficult refer to the solutions which are explained step by step to guide you to the correct answer.

Starting with a rather easy one

Moving towards a tougher one

To conclude

There was a purpose in providing you these problems and their solutions.

In all the three integration problems, particularly, the second one, it is to be noted that if you start out on the right track, then they are not very tough. But once you deviate and take a wrong route you will not be able to land at the correct answer easily and you may have to concede valuable time. So you are advised not to pounce upon the problem as soon as you see it. Wait for a while and try to guess the correct procedure. Once you are done with the guessing part, solve it.

You will observe that many integration formulae are similar and tend to mix up in your mind. So while memorizing them make a comparison of the similar looking formulae and also practise writing and verifying them regularly. You may prepare a formula chart for indefinite and definite integrals exclusively and consult it regularly. Develop a habit to try hard recollecting a formula before giving up and consulting the chart. This improves your memory.

So try this one from IITJEE, 2012 and be ready for next set of integration problems in my upcoming post:


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      Pranjal Shah 

      3 years ago


      Is the question 1/(secx+cotx) or 1/(sec^2x+cot^2x). I'll mention hint for both.

      If it's former, then change sec to cos, cot to cos and sin. Simplify. Put sinx=t. You will get t/(at^2+bt+c) form. Put t=A*d/dx(Denominator)+B. Done.

      If it's latter, then change sec^2x to 1+tan^2x and cot to 1/tan. Simplify. Put tanx = t. You will get t^2/(t^2+1)(t^4+t^2+1)dt. Factorise t^4... term and use partial fraction method to separate. Integrate. It will be a long question and these types aren't usually asked in competitive examinations.

      Best Wishes! :D

    • profile image

      Pranjal Shah 

      3 years ago

      Last one is surprisingly easy. Just put secx + tanx = t and calculate value of secx in terms of t and solve.

    • profile image


      3 years ago

      how to integrate 1/(sec^x+ cot ^x)

    • profile image


      4 years ago

      ok good one

    • profile image


      6 years ago

      The last one you can solve by integration by parts.

    • profile image


      7 years ago

      how did u solve the last (non solved) one??

    • profile image


      7 years ago

      how to solve tricky problem in integration & other once


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