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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.
DEFINITION: ANTIDERIVATIVE (INTEGRAL) For example, the function is an antiderivative of on interval because for each xin this interval . 331)(xxF2)(xxf),()(31)('23xfxxdxdxFHowever, is not the only antiderivative of f on this interval. If we add any constant C to , then the function 331)(xxF331x)(031)('23xfxCxdxdxGDefinition 5.2.1 (p. 322)