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chap7sec7

# chap7sec7 - 7.7 Approximate Integration ofdata, Forexample...

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7.7 Approximate Integration If you need to find a definite integral when it is impossible to find an antiderivative or when a function arises from a collection   of data, how do you go about finding the value of the definite integral? For example, 2 1 0 x e dx  can’t be calculated exactly through the various techniques of integration that we have been studying.  Riemann sums were studied earlier in this text as a method of finding an approximation for a definite integral. Any Riemann  sum can be used to evaluate a definite integral. To do this you must calculate a left endpoint approximation or a right endpoint  approximation. Look at Figure 1 on page 512. Another way to approximate a definite integral is with the  Midpoint Rule .  (Page 512). [ ] ( 29 [ ] 1 2 1 1 ( ) ( ) ( ) ( ) - where = 1 and midpoint of , 2 b n n a i i i i i f x dx M x f x f x f x b a x n x x x x x - - = ∆ + + + = + = L

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chap7sec7 - 7.7 Approximate Integration ofdata, Forexample...

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