# NCERT Solutions for Class 12 Maths Chapter 7

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

## NCERT Solutions for class 12 Maths Chapter 7

### 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.

##### Level 3 Test 1 Test 2
###### Previous Year’s Questions
1. Evaluate: [Delhi 2017]
2. Find [Delhi 2017]
3. Find [Delhi 2017]
4. Evaluate: [Delhi 2017]
5. Evaluate: [Delhi 2017]
6. Evaluate as limit of sums. [CBSE Sample Paper 2017]
7. Using properties of integral, evaluate [CBSE Sample Paper 2017]
8. Find: [CBSE Sample Paper 2017]
9. Find: [Delhi 2016]
10. Evaluate: [Delhi 2016]
11. Find: [Delhi 2016]
12. Evaluate: [Delhi 2016]

Methods of finding Integration: The following are the four important methods of integration.

1. Integration by decomposition into sum or difference.
2. Integration by substitution.
3. Integration by parts
4. 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.

#### 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.

## 4 thoughts on “NCERT Solutions for Class 12 Maths Chapter 7”

1. Vijay rai says:

Sir up board ka solution nahi dalate hai kya

2. Ranjeet says:

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

3. NAVYA says:

Very useful Sir Thank you

4. PARAMESWARAN says:

VERY VERY USEFULL