Indefinite Integrals

AP Calculus · Axiom Academy

Understanding antiderivatives and the general solution with +C A function F(x) is an antiderivative of f(x) if F'(x) = f(x) . The indefinite integral of f(x) is the family of all antiderivatives: The +C (constant of integration) is essential because many functions share the same derivative. dx indicates the variable of integration F(x) + C is the general antiderivative C is the constant of integration An antiderivative undoes a derivative: Always include +C for indefinite integrals To verify: differentiate your answer and check it equals the integrand If given an initial condition like F(0) = 5 , you can solve for C

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