Differential Equations For Dummies
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The Riemann Sum formula provides a precise definition of the definite integral as the limit of an infinite series. The Riemann Sum formula is as follows:

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Below are the steps for approximating an integral using six rectangles:

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  1. Increase the number of rectangles (n) to create a better approximation:

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  2. Simplify this formula by factoring out w from each term:

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  3. Use the summation symbol to make this formula even more compact:

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    The value w is the width of each rectangle:

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    Each h value is the height of a different rectangle:

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    So here is the Riemann Sum formula for approximating an integral using n rectangles:

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  4. For a better approximation, use the limit

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  5. to allow the number of rectangles to approach infinity:

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About This Article

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Steven Holzner was an award-winning author of more than 130 books, of which more than 2 million copies have been sold. His books have been translated into 23 languages. He served on the Physics faculty at Cornell University for more than a decade, teaching both Physics 101 and Physics 102. Holzner received his doctorate in physics from Cornell and performed his undergraduate work at Massachusetts Institute of Technology, where he also served as a faculty member.

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