Formal+Definition+of+Antiderivative+and+Indefinite+Integral

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 * Formal Definition of Antiderivative and Indefinite Integral

-If, then //g(x)// is the derivative of //f(x)// and //f(x)// is the antiderivative of //g(x)// --properties: ---important to remember: taking the derivative of f(x) may give you g(x), but taking the antiderivative of g(x) may not necessarily give you f(x) in its original form.---
 * Antiderivative/Indefinite Integral:**
 * The antiderivative of a derivative is the original function plus a constant.
 * Let f(x) be any antiderivative for g(x)
 * For any constant c, f(x)+c is an antiderivative for g(x)
 * Proof- since [[image:CodeCogsEqn_(14).gif width="209" height="28"]]
 * =f(x)+0 => f(x)
 * So f(x)+c is an antiderivative for g(x).



EX1: ---important to remember: the constant c is unknown. If the original function 3x^2 + c(any constant), the derivative of f(x) is 6x---

EX2:

EX3:


 * //Antiderivative List://**

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