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Lesson-16-filled

# Lesson-16-filled - Math 1314 Lesson 16 Antiderivatives So...

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Math 1314 Lesson 16 Antiderivatives So far in this course, we have been interested in finding derivatives and in the applications of derivatives. In this chapter, we will look at the reverse process. Here we will be given the “answer” and we’ll have to find the “problem.” This process is generally called integration . We can use integration to solve a variety of problems. Antiderivatives Definition : A function F is an antiderivative of f on interval I if ( ) ( ) F x f x = for all x in I. The process of finding an antiderivative is called antidifferentiation or finding an indefinite integral . Example 1 : Determine if F is an antiderivative of f if 5 2 2 3 3 1 ) ( 2 3 + + + = x x x x F and . 2 3 ) ( 2 + + = x x x f Example 2 : Suppose . 27 ) ( and 10 ) ( 3 3 - = + = x x K x x H If 2 3 ) ( x x f = , show that each of H and K is an antiderivative of f , and draw a conclusion.

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Notation : We will use the integral sign to indicate integration (antidifferentiation). Problems will be written in the form + = . ) ( ) ( C x F dx x f
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Lesson-16-filled - Math 1314 Lesson 16 Antiderivatives So...

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