NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.9 Integrals - PDF Download

NCERT solutions for class 12 maths chapter 7 exercise 7.9 Integrals covers an essential topic of determining the definite integral using substitution. This exercise has several questions that allow you to practice the substitution method for indefinite integrals. In NCERT solutions for class 12 maths chapter 7 exercise 7.9, you will be given a function in each of these problems and you have to use the " substitution method" to calculate the integral of it.

To solve these questions, you must comprehend the sequential procedure for utilizing the substitution method. Our subject experts of eSaral have explained this topic in simple and precise language so that you can get a deep understanding of the substitution method to find the definite integral of a given function and score good marks in exams. Ex 7.9 class 12 maths chapter 7 consists of 10 questions based on finding definite integrals by substitution method. By solving ex 7.9, you will get through with the concept of substitution. Class 12 maths chapter 7 exercise 7.9 NCERT solutions are provided here in free PDF format that can be downloaded by you from the official website of eSaral. 

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Topics Covered in Exercise 7.9 Class 12 Mathematics Questions

Ex 7.9 class 12 maths solutions covers an important topic of evaluation of definite integrals by substitution. You can find a detailed solution of this topic below.

1. Evaluation of Definite Integrals by Substitution

We have already covered a number of methods to determine the indefinite integral in earlier sections. The substitution method is an essential method for determining the indefinite integral. 

To evaluate $\int_a^b f(x) d x$ , by substitution, the steps could be as follows:

(i) Consider the integral without limits and substitute, y = f(x) or x = g(y) to reduce the given integral to a known form.

(ii) Integrate the new integrand with respect to the new variable without mentioning the constant of integration.

(iii) Resubstitute for the new variable and write the answer in terms of the original variable.

(iv) Find the values of answers obtained in (3) at the given limits of integral and find the difference of the values at the upper and lower limits.

Tips for Solving Exercise 7.9 Class 12 Chapter 7 Integrals

To determine the definite integrals by substitution method and solving questions in ex 7.9 class 12 maths ch 7 our subject experts of eSaral have explained some useful tips. 

1. This exercise requires you to have a perfect comprehension of the substitution method in order to turn the definite function into a familiar form whose integration can be calculated easily. You must study and comprehend the concept in order to solve NCERT solutions class 12 maths chapter 7 exercise 7.9. 
2. Students should practice a wide variety of questions in order to be able to accurately illustrate the substitution for a given definite function. 
3. Students should also practice examples given before the exercise 7.9 to comprehend the topic precisely.

Importance of Solving Ex 7.9 Class 12 Maths Chapter 7 Integrals

Students will get a lot of benefits by solving questions of ex 7.9 class 12 maths chapter 7 Integrals. 

1. Class 12 maths chapter 7 exercise 7.9 NCERT solutions provide in-depth knowledge of the substitution method for definite integrals which can be referred by the students for solving questions.
2. In NCERT solutions class 12 maths chapter 7 ex 7.9, there are some important questions related to substitution method that will help you in board examination.
3. Ex 7.9 class 12 maths chapter 7 has included examples and important questions. By solving these questions, you will gain a clear understanding of concepts.
4. NCERT solutions PDF will help you to solve questions in step by step manner.

Frequently Asked Questions

Question 1. What is meant by substitution in definite integration?

Answer 1. Integration by substitution is a method that is used when direct integration is not possible or the function to be integrated is a complex function. By changing the given function into a simpler function, this integration method by replacement simplifies the integral of a function. 

Question 2. Why do we use the substitution method?

Answer 2. We use integration by substitution method to find the solution of the given function where the normal integration methods fail.