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The concept of primitive

The concept of primitive MATH11007 NOTES 5: THE FUNDAMENTAL THEOREM OF CALCULUS 1 The concept of primitive Deﬁnition 1 1 We say that a function F : A → R is a primitive (or an anti- derivative or an indeﬁnite integral) of the function f : A → R if F is diﬀerentiable and F′= f Example 1 1 Let f : R → R be deﬁned by f(x) = xn n ∈ N

What is the de nition of a primitive?
De nition of primitive A function F is a primitive of a function f, or an antiderivative of f, if F 0 = f. The notation we use to denote this relationship is either (when working with a speci c, named function, given by a certain rule). number of important comments are in order about the de nition of a primitive.
Does a discontinuous function have a primitive function?
F 0( ) exists and is equal to f( ) for each 2 I, F is continuous on I. Theorem 4 (Continuous function has a primitive function). If f is continuous on I, then f has a primitive function F on I. Proof. Later. Can a discontinuous function have a primitive function? Yes. Example 1 (Discontinuous function with primitive function.). The function f : R !
Are primitive functions linear?
f. Due to the linearity of the derivative, primitive functions are also linear: Theorem 1 (Linearity of primitive functions). If F is a primitive function of f, and G is a primitive function of g on an interval I and ; 2 R, then the function
How do you express a primitive function using elementary functions?
1 P(x) 2. Thus, a primitive function R Q(x) equals to the sum of nitely many primitive functions of three types: where p(x) is a real polynomial, j 2 N and except x all other symbols are real constants, and 2 4 < 0. If we can express these primitive functions using elementary functions, we can express R P(x) using elementary functions Q(x) as well.

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