MATH22 NOTES

# MATH22 NOTES - ANTIDERIVATIVES (INTEGRAL) THE INDEFINITE...

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ANTIDERIVATIVES (INTEGRAL)

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THE INDEFINITE INTEGRAL AND THE BASIC INTEGRATION FORMULAS OBJECTIVES: know the relationship between differentiation and integration; identify and explain the different parts of the integral operation; and perform basic integration by applying the power formula and the properties of the indefinite integrals.
A function F is called an antiderivative (or integral) of the function f on a given open interval if F’(x) = f(x) for every value of x in the interval. FINITION: ANTIDERIVATIVE (INTEGRAL) For example, the function is an antiderivative of on interval because for each x in this interval . 3 3 1 ) ( x x F = 2 ) ( x x f = ) , ( + ∞ -∞ ) ( 3 1 ) ( ' 2 3 x f x x dx d x F = = = However, is not the only antiderivative of f on this interval. If we add any constant C to , then the function 3 3 1 ) ( x x F = 3 3 1 x ) ( 0 3 1 ) ( ' 2 3 x f x C x dx d x G = + = + =

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## MATH22 NOTES - ANTIDERIVATIVES (INTEGRAL) THE INDEFINITE...

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