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CBSE Notes for Class 12 Mathematics II chapter 7. Integrals: Introduction, quick revision notes for Class 12 Mathematics II chapter 7. Integrals Introduction, Chapter-wise CBSE Revision Notes, CBSE Notes PDF Free Download, CBSE One Liner Notes Class 12, Half Yearly Revision Notes, CBSE Revision Notes Class 12 Mathematics II
Get CBSE Notes for Class 12 Mathematics II Chapter 7. Integrals: Introduction prepared by experts as per the latest NCERT syllabus and CBSE exam pattern. These concise and easy-to-understand notes cover important definitions, formulas, diagrams, and key concepts from the chapter to help students in quick revision and effective exam preparation. Whether you are studying for school tests, board exams, or competitive exams, these notes provide a reliable study resource. Designed in simple language with point-wise explanations, they save time and enhance learning efficiency. Download free PDF notes, explore solved examples, and strengthen your understanding of [Topic Name] for scoring high marks. Perfect for Class 12 students who want clear, structured, and exam-oriented notes for CBSE Mathematics II.
Integrals
Introduction:
(i) Differential Calculus: Differential Calculus is centred on the concept of the derivative. The original motivation for the derivative was the problem of defining tangent lines to the graphs of functions and calculating the slope of such lines.
(ii) Integral Calculus: Integral Calculus is motivated by the problem of defining and calculating the area of the region bounded by the graph of the functions.
(iii) Anti Derivatives: The functions that could possibly have given function as a derivative are called anti derivatives (or primitive) of the function.
(iv) Integration: The formula that gives all these anti derivatives is called the indefinite integral of the function and such process of finding anti derivatives is called integration.
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.
The Fundamental Theorem of Calculus:
There is a connection, known as the Fundamental Theorem of Calculus, between indefinite integral and definite integral which makes the definite integral as a practical tool for science and engineering. The definite integral is also used to solve many interesting problems from various disciplines like economics, finance and probability.
The definite integral is used as a practical tool for:
(i) Science and Ingineering
(ii) Economics, finance and probability.
Integration as an Inverse Process of Differentiation
Integration is the inverse process of differentiation.
Instead of differentiating a function, we are given the derivative of a function and asked to find its primitive, i.e., the original function. Such a process is called integration or anti differentiation.
Exercise 7.1
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Ace your exams with CBSE Notes for Class 12 Mathematics II chapter 7. Integrals: Introduction. These notes provide a clear explanation of important concepts, formulas, diagrams, and solved examples from the NCERT syllabus. Specially designed for Class 12 students, the notes are structured in a simple, point-wise manner to make revision quick and effective. Whether you are preparing for school tests, board exams, or competitive exams, these Mathematics II notes will boost your confidence and save valuable study time. You can also download Mathematics II class 12 chapter 7. Integrals free PDF notes for offline learning. With easy-to-grasp language, exam tips, and well-organized content, these CBSE Mathematics II notes on chapter 7. Integrals – Introduction are the perfect study companion for scoring high marks and mastering the subject.
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