Differential Equations For Dummies
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Sigma notation comes in handy when you’re approximating the area under a curve. For example, express an 8-right-rectangle approximation of the area under


from 0 to 4 and compute the approximation.

  1. Express the basic idea of your sum:


This just means that you’re adding up the areas of 8 rectangles, each of which has an area of base times height.

  1. Figure the base and plug in.


Constants, like 1/2, can be pulled through the sigma symbol.

  1. Add the limits of summation, and express the height as a function of the index of summation:

Since each rectangle has a base of 1/2, the right edge of the first rectangle will be at 1/2; the right edge of the second rectangle will be at 2/2, or 1; the right edge of the third will be at 3/2, etc. That’s what the does above. If you plug 1 then 2 then 3, etc. up to 8 into i, you get the locations of the right edges of all 8 rectangles.

  1. Plug in your function,

  2. Simplify:

  3. Use the sum of squares rule to finish:


About This Article

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About the book author:

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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