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Understanding Antiderivatives in Calculus

Learn about antiderivatives and indefinite integration in calculus, including definitions, basic formulas, and solving equations to find general and particular solutions. Master the concept of antiderivatives and improve your integration skills today.

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Understanding Antiderivatives in Calculus

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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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