NCERT Solutions for class 12 Maths Chapter 7 Integrals Exercise 7.11, 7.10, 7.9, 7.8, 7.7, 7.6, 7.5, 7.4, 7.3, 7.2, 7.1 and Miscellaneous Exercises in English and Hindi Medium free to download in PDF free for new session 2022-23. UP Board students are also using NCERT Textbooks. So, download UP Board Solutions for Class 12 Maths Chapter 7 in PDF format free. Class 12 Maths NCERT solutions 2022-2023 and Solutions Apps solutions, previous years CBSE Board papers, important questions, assignment of integration, test papers etc.

## NCERT Solutions for Class 12 Maths Chapter 7

### Class 12 Maths Chapter 7 Solutions in English Medium

- Class 12 Maths Exercise 7.1 Solutions
- Class 12 Maths Exercise 7.2 Solutions
- Class 12 Maths Exercise 7.3 Solutions
- Class 12 Maths Exercise 7.4 Solutions
- Class 12 Maths Exercise 7.5 Solutions
- Class 12 Maths Exercise 7.6 Solutions
- Class 12 Maths Exercise 7.7 Solutions
- Class 12 Maths Exercise 7.8 Solutions
- Class 12 Maths Exercise 7.9 Solutions
- Class 12 Maths Exercise 7.10 Solutions
- Class 12 Maths Exercise 7.11 Solutions
- Class 12 Maths Miscellaneous Exercise 7

Class: 12 | Maths (English and Hindi Medium) |

Chapter 7: | Integrals |

### 12th Maths Chapter 7 Solutions

NCERT Solutions for class 12 Maths Chapter 7 in PDF format to free download. Download NCERT Books 2022-23 and offline apps based on latest CBSE Syllabus. Join the discussion forum to ask doubts related to education in NIOS or CBSE.

### Class 12 Maths Chapter 7 Solutions in Hindi Medium

- Class 12 Maths Exercise 7.1 Solution in Hindi
- Class 12 Maths Exercise 7.2 Solution in Hindi
- Class 12 Maths Exercise 7.3 Solution in Hindi
- Class 12 Maths Exercise 7.4 Solution in Hindi
- Class 12 Maths Exercise 7.5 Solution in Hindi
- Class 12 Maths Exercise 7.6 Solution in Hindi
- Class 12 Maths Exercise 7.7 Solution in Hindi
- Class 12 Maths Exercise 7.8 Solution in Hindi
- Class 12 Maths Exercise 7.9 Solution in Hindi
- Class 12 Maths Exercise 7.10 Solution in Hindi
- Class 12 Maths Exercise 7.11 Solution in Hindi
- Class 12 Maths Miscellaneous Exercise 7 Solution in Hindi

### Class 12 Maths Chapter 7 Solutions in PDF

- Download Class 12 Maths Exercise 7.1 in PDF
- Download Class 12 Maths Exercise 7.2 in PDF
- Download Class 12 Maths Exercise 7.3 in PDF
- Download Class 12 Maths Exercise 7.4 in PDF
- Download Class 12 Maths Exercise 7.5 in PDF
- Download Class 12 Maths Exercise 7.6 in PDF
- Download Class 12 Maths Exercise 7.7 in PDF
- Download Class 12 Maths Exercise 7.8 in PDF
- Download Class 12 Maths Exercise 7.9 in PDF
- Download Class 12 Maths Exercise 7.10 in PDF
- Download Class 12 Maths Exercise 7.11 in PDF
- Download Class 12 Maths Miscellaneous Exercise 7
- NCERT Book Class 12 Maths Chapter 7
- NCERT Book Class 12 Maths Answers
- Class 12 Maths Revision Book Chapter 7 Part 1
- Class 12 Maths Revision Book Chapter 7 Part 2
- Class 12 Maths Revision Book Chapter 7 Part 3
- Class 12 Maths Revision Book Answers
- Download Class 12 Maths Chapter 7 Assignment 1
- Download Class 12 Maths Chapter 7 Assignment 2
- Download Class 12 Maths Chapter 7 Assignment 2 Answers
- Download Class 12 Maths Chapter 7 Assignment 3
- Download Class 12 Maths Chapter 7 Assignment 4
- Class 12 Maths Solution Main Page

#### Class 12 Maths Chapter 7 Exercise 7.1 Solution in Videos

#### Class 12 Maths Chapter 7 Exercise 7.2 Solution in Videos

#### Class 12 Maths Chapter 7 Exercise 7.3 Solution in Videos

#### Class 12 Maths Chapter 7 Exercise 7.4 Solution in Videos

#### Class 12 Maths Chapter 7 Exercise 7.5 Solution in Videos

#### Class 12 Maths Chapter 7 Exercise 7.6 Solution in Videos

#### Class 12 Maths Chapter 7 Exercise 7.7 Solution in Videos

#### Class 12 Maths Chapter 7 Exercise 7.8 Solution in Videos

#### Class 12 Maths Chapter 7 Exercise 7.9 Solution in Videos

#### Class 12 Maths Chapter 7 Exercise 7.10 Solution in Videos

#### Class 12 Maths Chapter 7 Exercise 7.11 Solution in Videos

#### Class 12 Maths Chapter 7 Miscellaneous Solution in Videos

#### Methods of Integration

The following are the four important methods of integration:

- Integration by decomposition into sum or difference.
- Integration by substitution.
- Integration by parts
- Integration by successive reduction.

##### Historical Facts!

Integration is an operation inverse to derivatives. As per history of Maths, the concept of integrals comes earlier than the terms of derivatives. In fact the concept of integration owes different origin. It was mainly for problem of finding areas of plane regions, surface areas and volumes of solid bodies etc. Firstly the definite integral was used as a limit of a certain sum expressing the area of some region. Archimedes, Eudoxus and others developed it as a numerical value equal to the area under the curve. The word integration has originated from addition. The verb ‘to integrate’ means to merge. Later on, link between apparently two different concepts of derivatives and integrals was established. It was the well-known mathematician Newton and Leibnitz in 17th century. This relation is known as fundamental theorem of integral calculus. In the 19th century, Cauchy and Riemann developed the concept of Riemann integration.

Download NCERT Books for class 12 and Offline Apps 2022-23 based on new CBSE Syllabus. Ask your doubts related to NIOS or CBSE Board and share your knowledge with your friends and other users through Discussion Forum.

### Important Questions on 12th Maths Chapter 7

### What is anti derivatives of a function?

If a function f is differentiable in an interval I, i.e., its derivative f’ exists at each point of I, then functions f that could possibly have given function as a derivative are called anti derivatives (or primitive) of the function.

### What is integration?

The formula that gives all anti derivatives is called the indefinite integral of the function and such process of finding anti derivatives is called integration.

### What is Integral Calculus?

The development of integral calculus arises out of the efforts of solving the problems of the following types: (a) the problem of finding a function whenever its derivative is given, (b) the problem of finding the area bounded by the graph of a function under certain conditions. These two problems lead to the two forms of the integrals, e.g., indefinite and definite integrals, which together constitute the Integral Calculus.

### What is meant by integration constant C?

C is customarily referred to as arbitrary constant. In fact, C is the parameter by varying which one gets different anti derivatives (or integrals) of the given function.