AERO BOARD PREP 2014CALCULUSJGG DECENAIllustration•F(x) = x2 is an antiderivative of f(x) = 2x because F’(x)=f(x)•But so are G(x) = x2+ 2 and H(x) = x2– 7. Note that F, G and H differ only by a constant.•For any constant real number, C, the function F(x)=x2+ C is an antiderivative of f(x).
AERO BOARD PREP 2014CALCULUSJGG DECENASince the functions: G(x) = x2 F(x) = x2+ 2 H(x) = x2– 7 differ only by a constant, the slope of the tangent line remains the same The family of antiderivatives can be represented by F(x) + CFamily of Antiderivatives
AERO BOARD PREP 2014CALCULUSJGG DECENAThe family of all antiderivaties of f(x) is indicated by Integral signIntegrandThis is called the indefinite integral.The Indefinite IntegralIt is the most general antiderivative of f(x).f(x)dx
AERO BOARD PREP 2014CALCULUSJGG DECENAThe Indefinite Integral