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NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.4 Integrals - PDF Download

JEE Mains & Advanced

NCERT solutions for class 12 maths chapter 7 exercise 7.4 Integrals presents the application of particular functions, whose integration is commonly required. The questions of exercise 7.4 require the pre-calculated integration of a few common functions. In order to solve sums, students must go through the process of derivation of these functions. NCERT solutions for ex 7.4 class 12 maths chapter 7 are developed by the subject experts of eSaral to help you understand the concepts of this topic in precise and detailed manner. 

Class 12 maths chapter 7 exercise 7.4 NCERT solutions consist of 25 questions that all are based on some particular functions. You can also solve the questions by remembering the formulas used in this exercise. eSaral’s expert teachers have provided NCERT solutions in PDF format. These solution PDFs can be downloaded for free from the official website of eSaral that will help you to prepare for exams and score good marks. 

Topics Covered in Exercise 7.4 Class 12 Mathematics Questions

Ex 7.4 class 12 maths solutions covers some formulas of integrals and their applications.


Integrals of Some Particular Functions

  1.  Integrals of Some Particular Functions

Here, we have mentioned below some important formulas of integrals and apply them for integrating many other related standard integrals:

(i) $\int \frac{d x}{x^2-a^2}=\frac{1}{2 a} \log \left|\frac{x-a}{x+a}\right|+\mathrm{C}$

(ii) $\int \frac{d x}{a^2-x^2}=\frac{1}{2 a} \log \left|\frac{a+x}{a-x}\right|+C$

(iii) $\int \frac{d x}{x^2+a^2}=\frac{1}{a} \tan ^{-1} \frac{x}{a}+C$

(iv) $\int \frac{d x}{\sqrt{x^2-a^2}}=\log \left|x+\sqrt{x^2-a^2}\right|+C$

(v) $\int \frac{d x}{\sqrt{a^2-x^2}}=\sin ^{-1} \frac{x}{a}+\mathrm{C}$

(vi) $\int \frac{d x}{\sqrt{x^2+a^2}}=\log \left|x+\sqrt{x^2+a^2}\right|+C$

Tips for Solving Exercise 7.4 Class 12 Chapter 7 Integrals

You will be able to solve ex 7.4 class 12 maths chapter 7 by following the essential tips provided by expert teachers of eSaral.

  1. Students have to learn and remember all the formulas related to integrals before solving questions in ex 7.4 class 12 maths.

  2. Ex 7.4 class 12 maths ch 7 has solved examples which you must solve for clear understanding of the concepts.

  3. The formulas of particular functions in integrals must be revised frequently for proper learning of this topic.

Importance of Solving Ex 7.4 Class 12 Maths Chapter 7 Integrals 

There are a lot of advantages of solving questions in ex 7.4 class 12 maths chapter 7 Integrals. Here, our subject experts of eSaral have combined some of the essential benefits for solving ex 7.4 which you can check below.

  1. NCERT solutions for class 12 maths chapter 7 exercise 7.4 is highly recommended to solve questions for board exams. Students are advised to solve each question of the exercise that will help you to score high marks.

  2.  Every formula of integrals has been explained in detail and step by step in NCERT solutions for students to have deep comprehension of the questions asked in board exams.

  3. NCERT solutions not only provide exercise questions but examples, solve formulas with proof etc. so that you can grasp the concepts and feel confident during exams.

  4. The solution PDFs have accurate answers for all the questions of ex 7.4 that you can trust without any second thought. 

Frequently Asked Questions

Question 1. How many main formulas of integrals are explained in NCERT solutions class 12 maths chapter 7 ex 7.4?

Answer 1. There are a total of 6 main formulas of integrals explained in NCERT solutions class 12 maths chapter 7 ex 7.4. These formulas are provided above which you can study for solving questions in ex 7.4.

Question 2. Is exercise 7.4 important for class 12 maths board exams?

Answer 2. Yes, exercise 7.4 is very important for the students of class 12. The formula based question from this exercise is asked in class 12 board exams. Students must solve all the questions in ex 7.4 class 12 maths to achieve a high score in exams.



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