Standard Integrals

Brian Knight and Roger Adams
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Brian Knight: Goldsmiths’ College
Roger Adams: Thames Polytechnic

Chapter 12 in Calculus I, 1975, pp 80-85 from Springer

Abstract: Abstract In this section we shall deal with some techniques of integration, regarded as the inverse process to differentiation. By this we mean that the integral of a function f(x) is given by: ∫ f ( x ) d x = F ( x ) + c $$ \int {f\left( x \right)dx} = F\left( x \right) + c $$ where the derivative of F(x) is equal to the integrand of the integral, f(x). Notice that there are no limits yet defined for the integral here, and in this case it is called an indefinite integral: the right-hand side consequently contains an arbitrary constant c (which can take any value we like) since if the derivative of F(x) equals f(x) then so does the derivative of F(x) + c.

Date: 1975
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DOI: 10.1007/978-1-4615-6594-9_12

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