NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.2 Integrals - PDF Download

1. Methods of Integration

In the previous section, we discussed integrals of those functions which were readily obtainable from derivatives of some functions. It was based on inspection, i.e., on the search of a function F whose derivative is f which led us to the integral of f. Nevertheless, this inspection-based approach is not very appropriate for many functions. As a result, we have to develop new methods or approaches for figuring out the integrals by putting them into standard forms. Some of the essential methods are based on:

1. Integration by Substitution 

2. Integration using Partial Fractions 

3. Integration by Parts 

•  Integration by substitution

here, we discuss the integration by substitution method.

The given integral $\int f(x) d x$ can be transformed into another form by changing the independent variable x to t by substituting x = g(t).

Consider  $\mathrm{I}=\int f(x) d x$

Put x = g(t) so that dxdt = g′(t).

Then we write dx = g′(t) dt

Thus $\mathrm{I}=\int f(x) d x=\int f(g(t)) g^{\prime}(t) d t$

This change of variable formula is one of the important tools available in the name of integration by substitution. It is often important to guess what will be the useful substitution. Usually, we make a substitution for a function whose derivative also occurs in the integrand. 

Tips for Solving Exercise 7.2 Class 12 Chapter 7 Integrals

NCERT solutions provided by eSaral have combined some tips and techniques for solving ex 7.2 class 12 maths chapter 7 Integrals. 

1. Ex 7.2 class 12 maths chapter 7 NCERT solutions requires a precise knowledge to understand the function whose integration needs to be calculated and then determine the proper substitution technique so that the integration becomes simple. 

2. Additionally, students need to be skillful in combining integration and differentiation.

3. NCERT solutions would assist to practice a wide variety of questions in order to be able to predict properly what the substitution should be.

Importance of Solving Ex 7.2 Class 12 Maths Chapter 7 Integrals 

Solving questions in ex 7.2 class 12 maths chapter 7 will benefit you in many ways. Here, we have included some important benefits for solving this exercise.

1. NCERT solutions provided by experts of eSaral have explained the method of integration by substitution in simple and easy language so that you can understand the concept for solving exercise questions.

2. You can solve questions asked in exams if you solve all the questions of ex 7.2 class 12 maths as the exercise includes simple to complex and concept based questions.

3. By practicing questions again and again from NCERT solutions class 12 maths chapter7 ex 7.2, you can remember the methods properly that will benefit you in examination.

4. Solving questions in NCERT solutions will improve your problem solving skills.
   

Frequently Asked Questions

Question 1. What is the method of substitution?

Answer 1. A change in the variable of integration often reduces an integral to one of the fundamental integrals. The method in which we change the variable to some other variable is called the method of substitution. 

Question 2. Is exercise 7.2 essential for class 12 maths board exams?

Answer 2. Yes, exercise 7.2 class 12 maths chapter 7 is an essential for board exams. Questions related to method of substitution are included in the board exam paper. You must solve this exercise to prepare for the board exam.