chap7sec7

# chap7sec7 - 7.7 Approximate Integration If you need to find...

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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, can’t be calculated exactly through the various techniques of integration that we have been studying. 2 1 0 x ed x 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). [] () [] 12 11 () ( ) - where = 1 and midpoint of , 2 b nn a ii i i i fxd x M xfx fx ba x n xx x x x −− ≈= + + + =+ = L Example: 3 2 1 ln dx x Find the integral using the Midpoint Rule with n=4. Draw the graph with your calculator.

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chap7sec7 - 7.7 Approximate Integration If you need to find...

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