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Expert-verified Found in: Page 777 ### Calculus

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

See the step by step solution

## Step 1. Summary

• 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.

$A\left(x\right)={\int }_{0}^{x} f\left(x\right)dx$ ## Step 2. Continue

• Sigma Notation and Properties of sum.

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

• Calculating sums of areas of small rectangles using definite integral. $\begin{array}{l}{\int }_{0}^{x} f\left(x\right)dx=\underset{n\to \mathrm{\infty }}{lim} \sum _{k=1}^{n} f\left({c}_{k}\right)\mathrm{\Delta }x\\ \mathrm{\Delta }x=\frac{b-a}{n}\\ {c}_{k}=a+k\mathrm{\Delta }x\end{array}$

Thus, the area under a curve, sigma notation and limits of sums can be reviewed. ### Want to see more solutions like these? 