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- W2477595129 abstract "This chapter focuses on the integration of functions. If the function f ( x ) is continuous at every point of the interval [ a , b ], then its primitive exists and is continuous at every point of that interval. If the function f ( x ) has discontinuities at certain points of the interval [ a , b ], then its primitive exists and is continuous everywhere in [ a , b ] except, perhaps, at points of discontinuity of f ( x ). The general expression F ( x ) + C , where C is an arbitrary constant for all primitives of the given function f ( x ) is called its indefinite integral F ( x ) + C = ∫ f ( x ) dx . The indefinite integrals of the principal elementary functions can be obtained by the inversion of the formulae for derivatives. The chapter discusses the integration of elementary functions. The integral of a rational function is either rational or is represented by a sum of a rational function and a finite number of logarithms and arctangents of rational functions with constant coefficients in front of the sign of logarithm and arctangent." @default.
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- W2477595129 date "1965-01-01" @default.
- W2477595129 modified "2023-09-24" @default.
- W2477595129 title "THE INTEGRATION OF FUNCTIONS" @default.
- W2477595129 doi "https://doi.org/10.1016/b978-0-08-011011-0.50009-4" @default.
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