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July 1st, 2017, 05:36 AM   #1
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Definite integral via Taylor/MacLaurin series

Hello

Over what range may I calculate definite integrals via these series'. For instance, a Maclaurin series is 'centred' around x = 0 and the function will have its best 'fit' at x = 0; surely this will make integrals over a wide range of x (say between 0 and 1000) inaccurate?

I cannot seem to find any information on this. Hope it makes sense!

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July 1st, 2017, 02:39 PM   #2
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It very much depends on the nature of the the function. In any case, it will be a question of how fast the integrated series converges.
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