Integration anti-derivative is an operation inverse to differentiation. From the historical point of Byjus Maths Class 8 Chapter 9 Cas Byjus Maths Class 8 Chapter 9 Cas 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 cqs plane regions, surface areas and Byjus Maths Class 8 Chapter 9 Cas volumes of solid byjus maths class 8 chapter 9 cas.
Archimedes, Eudoxus and others developed it as a numerical value equal to the area under the curve of a function for some interval. Later on, link between apparently two different concepts of differentiation and integration was established by well-known mathematician Newton and Leibnitz in 17th century.Byjus Maths Class 8 Chapter 9 Cas
This relation is known as fundamental theorem of integral calculus. In the 19th century, Cauchy and Riemann developed the concept of Riemann integration.
The Byjus Maths Class 8 Chapter 9 Cas Byjus Maths Class 8 Chapter 9 Cas following are the four important methods of integration: Integration Byjus Maths Class 8 Chapter 9 Cas Byjus Maths Class 8 Chapter 9 Cas by decomposition into sum or difference. Integration by substitution. Integration Byjus Maths Class 8 Chapter 9 Cas by parts Integration by successive reduction.
Important Dhapter on 12th Maths Chapter 7 What is anti derivatives of a function? If a function f is differentiable in an interval I, i. What caas integration? The formula that gives all anti derivatives is Byjus Maths Class 8 Chapter 9 Cas 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. What is meant by integration constant C? Byjus maths class 8 chapter 9 cas 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. Application of Integrals �.
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