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

NCERT solutions for class 12 maths chapter 7 exercise 7.7 Integrals includes questions based on a particular kind of integral learning. This section discusses a few specific kinds of standard integrals that are based on the method of integration by parts. Students will gain an understanding of this method by solving questions of ex 7.7. Our academic team of mathematics have provided a deep knowledge of solving questions by a particular type of integral in this exercise that will help you in preparing for board exams.

Class 12 maths chapter 7 exercise 7.7 NCERT solution consists of 11 questions based on the topic mentioned above. In this exercise, 9 questions are long answer types that require calculations, and the remaining two are multiple-choice questions. You will be able to solve these questions by the help of NCERT solutions developed by subject experts of eSaral.

Ex 7.7 class 12 maths chapter 7 is also available in downloadable PDF format at eSaral. You can download these free PDFs from the official website of eSaral and practice ex 7.7 class 12 maths to score good marks in exams. Here is the link below to download the free PDF of NCERT solutions.

## Topics Covered in Exercise 7.7 Class 12 Mathematics Questions

Ex 7.7 class 12 maths solutions covers the topic of integrals of some more types. You can check these particular types of standard integrals below.

 1 Integrals of some more types
1.  Integrals of some more types

Here, we discuss some special types of standard integrals based on the technique of integration by parts:

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

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

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

## Tips for Solving Exercise 7.7 Class 12 Chapter 7 Integrals

NCERT solutions for ex 7.7 class 12 maths chapter 7 will guide students to use the tips in which a specific type of function can be integrated.

1. In order to solve these specific integral forms and use the integration by part method, you must have a solid grasp of the previous exercise and a basic understanding of the associated rules.

2. The steps for solving these integrals of special functions should be closely followed by students. The probability of making mistakes will be decreased by carefully following these steps.

3. Through solving numerous problems in the exercise, students will gain the knowledge and proficiency to simplify the functions into a form that is simple to integrate.

## Importance of Solving Ex 7.7 Class 12 Maths Chapter 7 Integrals

There are a lot of benefits of solving questions in ex 7.7 class 12 maths chapter 7 Integrals. Our experts of eSaral have provided some of them that will help you in many ways.

1. In ex 7.7 class 12 maths ch 7, all the questions are solved by eSaral’s expert teachers in step by step method to provide clear understanding of standard integrals.

2. The topic of some special types of standard integrals are explained in a simple and detailed manner that will help you to solve questions with ease in board exams.

3. NCERT solution PDF for ex 7.7 class 12 maths has included answers for all the questions in sequential manner. You can cross check your answers with the solution PDF.

4. Practicing questions in NCERT solutions class 12 maths chapter 7 ex 7.7 will improve your time management skills and provide accuracy in solving questions.