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4.1 Antiderivatives and Indefinite Integration

4.1 Antiderivatives and Indefinite Integration. Definition of Antiderivative: A function F is called an antiderivative of the function f if for every x in the domain of f F’(x) = f(x) so, dy = f(x) dx. Integration is denoted by an integral sign. Constant of Integration.

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4.1 Antiderivatives and Indefinite Integration

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  1. 4.1 Antiderivatives and Indefinite Integration Definition of Antiderivative: A function F is called an antiderivative of the function f if for every x in the domain of f F’(x) = f(x) so, dy = f(x) dx Integration is denoted by an integral sign . Constant of Integration Integrand Variable of Integration F’(x) also = f(x) (first derivative)

  2. Basic Integration Formulas

  3. Integrate

  4. Rewriting before integrating

  5. Find the general solution of the equation F’(x) = and find the particular solution given the point F(1) = 0. Now plug in (1,0) and solve for C. 0 = -1 + C Final answer. C = 1

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