Integrals

Integral is process of getting a function from its derivative. Integral calculus is used due to the efforts of solving the problems of the following types: (a) the problem of finding a function if its derivative is given, (b) the problem of finding the area bounded by the graph of a function under certain conditions. Properties: 1. The derivative of an integral is the integrand itself. 2. Two indefinite integrals with the same derivative lead to the same family of curves and so they are equivalent. 3. The integral of the sum or difference of a finite number of functions is equal to the sum or difference of the integrals of the individual functions. 4. The constant can be taken outside the integral sign. 5. Properties 3 and 4 can be generalized to a finite number of functions. We introduce definite integral in two ways: a. As the limit of a sum b. As the difference between the values of its anti-derivative at the end points. Keywords: Standard Formulae; Geometrical Interpretation of Indefinite Integral, Properties of Indefinite Integral, Method of Inspection, Comparison between Differentiation and Integration, Fundamental Theorem of Calculus, First Fundamental Theorem of Calculus, Second Fundamental Theorem of Calculus, Integral by Substitution, Properties of Definite Integral, Some Special Type of Integrals,

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