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# Integrals Made Easy-A Class 12 Student's Perspective

Updated: Oct 22, 2023

## How to learn Integral Calculus for Class 12 Mathematics

I am a mathematics educator and teacher having taught Maths for three decades to High school and college students. You may be a little wary of Integration, but if you follow the techniques outlined here, I assure you that you'll sail through Integration. So, let's learn integral Calculus for Class 12 Maths.

### How to start learning Integration for Class 12?

Basically, integration and differentiation are a pair of inverse operations. Integral of a function is also called the anti derivative of the function. You'll start with the study of Indefinite integrals. There are a few basic formulas of Integration which you need to start with.

#### ​ ​What is the Substitution method in Integration?

Note that for indefinite integrals, we add the constant c, which is just the integration constant. The most basic method of Integration is using the Substitution method. Once you master this method, then you can basically solve any problem on Integration.

#### ​What happens when the degree of the Numerator is greater than or equal to degree of the denominator? ​

Next, what you'll need to know is how to integrate quotient functions. There are two cases here. Firstly when the degree of the numerator is greater than or equal to the degree of the denominator. In this case, you divide the numerator by the denominator and write the quotient and remainder. You will then proceed to integrate using the formula given. The methods are illustrated in my video links below.

##### What are Partial Fractions in Integration?

In case, you still need help, you can contact me for an online session on Integration. When the degree of the numerator is lesser than the degree of the denominator, you'll use the method of partial fractions. Again, keep in mind, that there are at least 4 cases which you need to know, that is, when the roots are distinct, repeated or complex.

You'll then move on to learn four standard integrals, namely tan, cot, cosec and sec and solve problems based on these.You also have special cases of the form linear/quadratic or linear/sqrt(quadratic). These two are more or less similar in solving.

###### ​How will you integrate Trigonometric Functions? ​

Next, you'll learn how to integrate rational functions of sinx and cosx . As a special type you'll also learn how to integrate functions of the form (asinx+bcosx)/(csinx+dcosx). There's another special type of integral where only even powers of x occur both in the numerator and denominator. Basically, you have degree two in the numerator and degree 4 in the denominator.

###### What is Integration by parts?

The next important topic that you'll learn is Integration by parts. Note that you need to remember the order of the functions while integrating by parts. ILATE OR LIATE. There's an exception to this rule and that's discussed in the links below.There's also a special form of integration by parts, involving the exponential function which is equally important.

###### How to use limits to calculate integral as a sum?

There are three more standard integrals which are useful while solving problems involving area of bounded regions. We now move to Definite Integrals. You'll learn how to integrate definite integral as the limit of a sum.

Tips on how to understand Integral as the limit of a Sum As of now, this topic has been excluded from the syllabus for 2024. You'll learn the Fundamental Theorem of Integral Calculus, using which you'll learn to evaluate Definite Integrals. You'll see how the Substitution method is applied for definite Integrals.

Keep in mind that when you use the Substitution method in definite integrals, the limit also changes. Last but not the least, you'll learn Properties of Definite Integrals. These properties are extensively used in problem solving.

Question on Definite Integrals These are the basic topics that you'll need to learn in Integration. I have provided a number of free resources, in the form of videos and multiple choice questions below. Feel free to make use of these.

###### What if you still need that little extra help?

In case you need more help, you can contact me for online tutoring. You can choose specific topics or the entire syllabus. Again, if you have any fellow students from your school, you can bring them along. I can help prepare you for the conceptual and case study based questions . My students have always excelled in Maths. So, let's start learning!