NCERT Solutions for Class 12 Maths Chapter 7 Integrals (Ex 7.6) Exercise 7.6

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NCERT Solutions for Class 12 Maths Chapter 7 Integrals (Ex 7.6) Exercise 7.6

Exercise 7.6 is an essential exercise from NCERT Class 12 Maths syllabus. The topics present in Exercise 7.6 Maths Class 12 are mainly integration with primary and crucial methods. Integration methods include partial fraction integration, integration by substitution and parts. Exercise 7.6 Class 12 Maths entirely has problems on integrals under the section of integration by factors. Class 12 NCERT Solutions for Maths question and answer set is divided into part 1 and part 2 with a solution book. NCERT Class 12 Maths has a total of 13 chapters. Here, we have provided the solutions for Exercise 7.6 Maths Class 12. The answers will help you prepare for the final examination. Our expert faculty have solved Exercise 7.6 Class 12 Maths as per the latest CBSE guidelines and syllabus.


List of Topics Covered Under NCERT Solutions for Class 12 Maths Chapter 7- Integrals 

Introduction

Integration as an Inverse Process of Differentiation

Methods of Integration

Integrals of some Particular Functions

Integration by Partial Fractions

Integration by Parts

Definite Integral

Fundamental Theorem of Calculus

Evaluation of Definite Integrals by Substitution

Some Properties of Definite Integrals


About Integration by Parts

The Integration is the inverse form of differentiation. If an equation has two integral functions like U and V with a single variable x. Then we can integrate the function with the Integration by parts method. 


The formula for differentiation, which has two functions with a single variable is. 


\[ \frac{d}{dx} (uv) = u \frac{dv}{dx} + v \frac{du}{dx} \]


The formula for Integration by Parts


uv = \[\int u\frac{\mathrm{dv} }{\mathrm{d} x} dx + \int v\frac{\mathrm{du} }{\mathrm{d} x}dx\]

This equation can be also written as\[ uv = uv{}'+ vu{}'\]

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What is There in Exercise 7.6 Class 12 NCERT Solutions?

Math is a complicated subject, and so is integration. Unless you understand all the steps correctly, you won't solve the problems. If you are a complete beginner in integration or face considerable difficulties in Ex 7.6 Class 12 Maths NCERT, then we have the ultimate solution for your understanding. The best guide for you is Exercise 7.6 Class 12 NCERT Solutions if you want to learn integrals. The content of the NCERT book is as per the latest CBSE syllabus and of high quality. However, the language is straightforward and concise so that the reader grasps it quickly. The matter available in the book is entirely reliable.

The easy language makes the book more viable and user-friendly. 7.1 is about the introduction. Again, 7.2 is about integration through the reverse procedure of differentiation. While 7.3 discusses the different methods of integration. 7.4 has integrals of specific functions, and 7.5 has integration with partial functions. NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6 integration by parts. 7.7 and 7.8 have definite integral and fundamental calculus theorem respectively. 7.9 talks about evaluating definite integrals with substitution method and 7.10 have some essential properties of definite integrals.

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What Is Integration by Parts of Ex 7.6?

Integration by parts usually teaches a student to solve the product's integration of any two or more functions. It is also known as the partial integration method. Here, we can write d(fa fb)/dx = fa d(fb)/dx + fb d(fa)/dx, where fa and fb are two different functions for a singular variable x. Here, you will also learn how to apply the integral on both sides. Finally, the product of both functions can be integrated by (first function) * (second function integral) – integral of ( first function of differential coefficient) * (second function on integration).

In all Class 12 Maths NCERT Solutions Chapter 7 Exercise 7.6 deals with displacement and volume by putting numbers into functions. Integrals are one of the main applications of calculus, which was hand-in-hand with differentiation and inverse proportion. Every problem clears your concepts in detail. Hence, one should continue to practice every day for good results. Maths require continuous hard work and practice.


NCERT Solutions for Class 12 Maths PDF Download

 

Chapter 7 - Integrals Exercises in PDF Format

Exercise 7.1

22 Questions & Solutions (21 Short Answers, 1 MCQs)

Exercise 7.2

39 Questions & Solutions (37 Short Answers, 2 MCQs)

Exercise 7.3

24 Questions & Solutions (22 Short Answers, 2 MCQs)

Exercise 7.4

25 Questions & Solutions (23 Short Answers, 2 MCQs)

Exercise 7.5

23 Questions & Solutions (21 Short Answers, 2 MCQs)

Exercise 7.6

24 Questions & Solutions (22 Short Answers, 2 MCQs)

Exercise 7.7

11 Questions & Solutions (9 Short Answers, 2 MCQs)

Exercise 7.8

6 Questions & Solutions (6 Short Answers)

Exercise 7.9

22 Questions & Solutions (20 Short Answers, 2 MCQs)

Exercise 7.10

10 Questions & Solutions (8 Short Answers, 2 MCQs)

Exercise 7.11

21 Questions & Solutions (19 Short Answers, 2 MCQs)


Students can also download the following additional study material -

How Class 12 Maths Chapter 7 Exercise 7.6 Help Students?

Students find Exercise 7.6 Class 12 NCERT solutions helpful because the content is written by expert teachers and professionals who have extensive experience in the education field. Teachers from the entire country and different parts of the world give their input to create unique content on Class 12 Maths ch 7 Ex 7.6. There are times when textbooks are not enough to help you clear your concepts. Here you need external help. While Class 12 Maths 7.6 Solutions allow one to earn their ideas for better understanding. Instead of attending tuitions at coaching centres, wasting money and time, you can get all the study materials at your fingertips. Here you can get the complete authentic Class 12 Maths Chapter 7 Exercise 7.6 solutions. It helps boost the student's confidence before exams and understand how to manage their time. You get to know which questions you have to practice more.

Solved Examples

Question1: Why is Class 12 Calculus Complicated?

Answer: Class 12 Calculus is difficult for beginners. However, once you understand the chapter, it becomes one of the most exciting chapters to solve.

Question2: What does NCERT Solutions Maths Class 12 Chapter 7 Cover?

Answer: Maths Class 12 Chapter 7 is all about integrals, partial fraction, integration, integration by parts and other forms.

FAQs (Frequently Asked Questions)

Q1. What are the Advantages of Ex 7.6 Class 12 Maths NCERT Solutions?

Ans: Not only study material, but you also have extra exercises to practice. The first step to do is read the entire Ex 7.6 Class 12 Maths Solutions and learn the concepts. Then you can easily copy down some of the solved examples from the material. All the sums are done following a good number of steps. If you don't follow the same steps for exams, then you will not score good marks. In Ex 7.6 Class 12 Maths Solutions, there is step marking. Hence you need to do all the correct steps and get the proper answer to achieve full marks. Using shortcut methods to arrive at the final answer somehow won't fetch you marks. There are 24 solutions with questions in Maths NCERT Solutions Class 12 Chapter 7 Exercise 7.6. Other activities also have solutions.

Q2. How to Differentiate Between Indefinite and Definite Integrals from Maths NCERT Class 12 Ex 7.6 Solutions?

Ans: Definite integrals are those which have both lower and upper limits given for an integral. In reality, you are calculating the area under the curve of x = c and x = d for function f(x) with a lower limit as c and an upper limit as b. For indefinite integrals, no upper or lower limits are provided. Here x can have a range of solutions because you calculate a general solution for a family of the same functions like f(x). In indefinite integrals, we need to add a fixed constant c, and the notation is written along with the solution we get. So this is the fundamental difference between definite and indefinite integrals of Exercise 7.6 Class 12 Maths NCERT solutions.

Q3. Where can I find NCERT Solutions for Exercise 7.6 of Chapter 7 of Class 12 Maths?

Ans: NCERT Solutions for all classes and subjects can be easily found on Vedantu. These solutions have been provided by various subject experts at Vedantu to help students who may need some assistance in answering questions that are provided in the NCERT Books. The solutions are specially written in a language that students can easily understand. You can find the NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.6 on Vedantu. These solutions are available at free of cost on Vedantu website(vedantu.com) and mobile app as well.

Q4. Is it important to practise examples given in Exercise 7.6 of Chapter 7 of Class 12 Maths?

Ans: Examples provided in the Exercise 7.6 of Chapter 7 of Class 12 Maths hold equal importance as the other questions in various exercises. Often questions based on the examples are asked in the exams and hence, practicing them will help you avoid losing any marks. Most of the questions in exercises are also based on these examples and practicing the examples will help you understand and solve the exercises easily.

Q5. How many questions are there in the NCERT Solutions for Exercise 7.6 of Chapter 7 of Class 12 Maths?

Ans: The NCERT Solutions for Exercise 7.6 of Chapter 7 of Class 12 Maths available on Vedantu include a total of 24 questions. Students can find step-by-step solutions for each of these questions in simple language designed to enhance their understanding of the various concepts that are a part of Chapter 7. You can also find and download chapter-wise solutions for all other exercises provided by Vedantu on its official website. These solutions are available at free of cost on Vedantu website(vedantu.com) and mobile app as well.

Q6. Is NCERT Solutions for Exercise 7.6 difficult?

Ans: No, it is not difficult. You need to practice regularly and enhance your clarity of the concepts of this chapter. Make sure you have a good grip on this exercise and you revise everything that is taught in school daily. Make sure to refer to Vedantu’s NCERT solutions, revision notes and important questions of Class 12 Maths Chapter 7 Exercise 7.6. These are prepared by subject matter experts and are 100% accurate.

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