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Expert-verifiedFound in: Page 777

Book edition
1st

Author(s)
Peter Kohn, Laura Taalman

Pages
1155 pages

ISBN
9781429241861

Read the section and make your own summary of the material.

The area under a curve, sigma notation and limits of sums can be reviewed

- Sigma Notation and Properties of sum.
- Limits of sum, and definition of definite integral.

A study of the accumulation function.

- The accumulation function A(x) gives the accumulation of area between the horizontal axis and the graph f(x) between 0 to x.

$A\left(x\right)={\int}_{0}^{x}\u200af\left(x\right)dx$

- Sigma Notation and Properties of sum.

$\sum _{k=\text{starting\_value}}^{\text{ending\_value}}\u200a\left(\text{function \_ of \_}k\right)\phantom{\rule{0ex}{0ex}}\text{1.}\sum _{k=1}^{n}\u200a\left({a}_{k}+{b}_{k}\right)=\sum _{k=1}^{n}\u200a{a}_{k}+\sum _{k=1}^{n}\u200a{b}_{k}\phantom{\rule{0ex}{0ex}}\text{2.}\sum _{k=1}^{n}\u200a{a}_{k}=\sum _{k=1}^{p-1}\u200a{a}_{k}+\sum _{k=p}^{n}\u200a{a}_{k}$

- Calculating sums of areas of small rectangles using definite integral.

$\begin{array}{l}{\int}_{0}^{x}\u200af\left(x\right)dx=\underset{n\to \mathrm{\infty}}{lim}\u200a\sum _{k=1}^{n}\u200af\left({c}_{k}\right)\mathrm{\Delta}x\\ \mathrm{\Delta}x=\frac{b-a}{n}\\ {c}_{k}=a+k\mathrm{\Delta}x\end{array}$

Thus, the area under a curve, sigma notation and limits of sums can be reviewed.

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