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 & miscellaneous exercises of Integrals in PDF form free download to use offline. Class 12 Maths NCERT solutions & other subject’s solutions with previous years CBSE Board papers, important questions, assignment of integration, test papers etc. For physical education’s notes and study material, click here.

NCERT Solutions for class 12 Maths Chapter 7

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Class 12 Maths Solutions – Integrals

• Exercise 7.1
• Exercise 7.2
• Exercise 7.3
• Exercise 7.4
• Exercise 7.5
• Exercise 7.6
• Exercise 7.7
• Exercise 7.8
• Exercise 7.9
• Exercise 7.10
• Exercise 7.11
• Miscellaneous

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

• NCERT Book
• NCERT Book Answers

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

• Revision Book 1        Revision Book 2       Revision Book 3
  
• Revision Book Answers

Assignments for practice

• Assignment 1
• Assignment 2        Answers
• Assignment 3
• Assignment 4

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

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.