NCERT Solutions for Class 12 Maths Chapter 7 Integrals

Class XII Mathematics Chapter 7 Exercise 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 language for new session. UP Board students are also using NCERT Textbooks. So, download UP Board Solutions for Class 12 Maths Chapter 7 in PDF format free. Get here Class 12 Maths NCERT solutions Apps, Extra practice questions, previous years CBSE Board papers, important questions, assignment of integration, test papers etc.

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.

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.

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