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Calculus

Found in: Page 777

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

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

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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.

$A (x) = \int_{0}^{x} f (x) d x$

Step 2. Continue

Sigma Notation and Properties of sum.

$\sum_{k = starting_value}^{ending_value} (function _ of _k) 1. \sum_{k = 1}^{n} (a_{k} + b_{k}) = \sum_{k = 1}^{n} a_{k} + \sum_{k = 1}^{n} b_{k} 2. \sum_{k = 1}^{n} a_{k} = \sum_{k = 1}^{p - 1} a_{k} + \sum_{k = p}^{n} a_{k}$

Calculating sums of areas of small rectangles using definite integral.

$\begin{array}{l} \int_{0}^{x} f (x) d x = lim_{n \to \infty} \sum_{k = 1}^{n} f (c_{k}) Δ x \\ Δ x = \frac{b - a}{n} \\ c_{k} = a + k Δ x \end{array}$

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

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