NCERT Solutions for class 12 Maths Chapter 7 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 of Integrals in English and हिंदी मीडियम free to download in PDF or use online. Class 12 Maths NCERT solutions & Solutions Apps solutions and previous years CBSE Board papers, important questions, assignment of integration, test papers etc. For NCERT Books, Click Here.

Class: | 12 |

Subject: | Maths – गणित |

Chapter 7: | Integrals |

Table of Contents

## NCERT Solutions for class 12 Maths Chapter 7

Back to NCERT Solutions Class 12 Maths

**Class 12 Maths Solutions – Integrals**

**Class 12 Maths Solutions – Integrals**

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

**NCERT Chapter to study online and answers given in the end of ncert books.**

*These books are very good for revision and more practice. These book are also confined to NCERT Syllabus.*

**Assignments for practice**

**Assignments for practice**

**Level 1 Test 1 Test 2 Test 3 Test 4 **

**Level 2 Test 1 Test 2**

**Level 3 Test 1 Test 2**

###### Previous Year’s Questions

**Evaluate**: [Delhi 2017]**Find**[Delhi 2017]**Find**[Delhi 2017]**Evaluate:**[Delhi 2017]**Evaluate:**[Delhi 2017]**Evaluate****as limit of sums.**[CBSE Sample Paper 2017]**Using properties of integral, evaluate**[CBSE Sample Paper 2017]**Find:**[CBSE Sample Paper 2017]**Find:**[Delhi 2016]**Evaluate:**[Delhi 2016]**Find:**[Delhi 2016]**Evaluate:**[Delhi 2016]

Methods of finding 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.

Table of Contents

#### What is anti derivatives of a function?

#### What is integration?

process of finding anti derivatives is called integration.

#### What is Integral Calculus?

(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.

Sir up board ka solution nahi dalate hai kya

thnx sir aapne itni mehnat se ye sab kuch upoad kiya thnx once again sir..

Its a big deal q ki mujhe bohot kam cheeze hi passand aati hai

Very useful Sir Thank you

VERY VERY USEFULL