# NCERT Solutions for Class 12 Maths Chapter 7

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 2020-21.

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## NCERT Solutions for Class 12 Maths Chapter 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 form to free download. Download NCERT Books 2020-21 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 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 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 (anti-derivative) is an operation inverse to differentiation. From the historical point of view, the concept of integration originated earlier than the concept of differentiation. In fact the concept of integration owes its origin to the problem of finding areas of plane regions, surface areas and volumes of solid bodies etc. firstly the definite integral was expressed 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 of a function for some interval. The word integration has originated from addition and the verb ‘to integrate’ means to merge. Later on, link between apparently two different concepts of differentiation and integration was established by 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.

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### Important Questions on 12th Maths Chapter 7

process of finding anti derivatives is called integration.

(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.