Topic 1: Antiderivatives
Section 5.1 Antiderivatives and Indefinite IntegralsTopic 1: Antiderivatives Theorem If the derivatives of two functions are equal on an open interval , then the functions differ by at most a constant. Symbolically, if F and G are differentiable functions on the interval and for all x in , then for some constant k.A function F is an antiderivative of a function f if . The notation is called the indefinite integral and is used to represent the family of all antiderivatives of . If we write .The symbol is called the integral sign and is called the integrand. The symbol indicates that the antidifferentiation is performed with respect to the variable x. The arbitrary constant C is called the constant of integration. Topic 2: Formulas and Properties of Indefinite IntegralsIndefinite Integrals of Basic FunctionsFor C, a constant, the following formulas are true: , , Properties: Indefinite IntegralsFor k, a constant, the following properties are ic 3: Applications ................
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