Let’s head up to the second portion of the Calculus portion of JEE Syllabus. The tricks that we have mastered and used while doing the differential part of calculus shall help a lot in Integral Calculus. After all, Integration is just the inverse of Differentiation. However, it gets a bit more interesting than that. Differentiation of functions can be easy, sometimes even implicit. However, Integration for the most part is not elementary. Let’s head on to the individual chapters and the books that we are going to need for this high-weightage unit of JEE Maths syllabus.
Chapter – Wise Analysis
- Integration : One of the toughest chapters in the entire mathematics syllabus simply because of the large amount of memorization involved. There are standard tricks, tips and methods that you have to keep at your tips if you want to stand a chance at solving questions of this chapter. Things like Method of Substitution and the use of Trigonometric Identities help a lot in simplifying questions. Integration by Parts is another important concept. As this chapter hosts a lot of concepts, it is tough to decipher which method would be needed to solve a given question. As such, doing a lot of practice becomes essential. Also, there are a ton of properties of Definite Integrals that are extremely helpful.
- Differential Equations : Differential Equations are all about applying the concepts that you have learnt and mastered under the chapter of Integration. A few terms and a bit of theory is to be remembered initially. However, other than that all questions reduce to an Indefinite Integration, with or without initial conditions. Note that few forms are to be remembered as is, like the Homogenous differential equation form and the Linear Differential Equation form. Also, origin shifting comes handy in reducing certain questions to Homogenous form.
- Area Under the Curve : By far the easiest chapter of this unit. Area under the curve is essentially definite integration with the proper limits as needed by question. Just realizing that a definite integral signifies area of the function with the co-ordinate axis helps in understanding this chapter. Other than that, this chapter has a few standard areas that are helpful if memorized.
Books You’ll Be Needing
All the best !