NCERT Solutions for class 12 Maths Chapter 7 Integrals in Hindi and English Medium updated for CBSE session 2022-2023.

NCERT Solutions for Class 12 Maths Chapter 7

Class XII Mathematics 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 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.

Class: 12Mathematics
Chapter 7:Integrals
Content:NCERT Exercises Solution
Content Type:Text, PDF and Videos Format
Medium:English and Hindi Medium
Methods of 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.

Important Questions on 12th Maths Chapter 7

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.

Historical Facts! about Integration

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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