87440196-MATH22-Powerpoint - ANTIDERIVATIVES(INTEGRAL THE INDEFINITE INTEGRAL AND THE BASIC INTEGRATION FORMULAS OBJECTIVES know the relationship

87440196-MATH22-Powerpoint - ANTIDERIVATIVES(INTEGRAL THE...

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ANTIDERIVATIVES (INTEGRAL)
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.
DEFINITION: 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 Definition 5.2.1 (p. 322)