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High School Math Calculus Precalculus with Limits: A Graphing Approach

Approximate the area of the region using the rectangles of equal width shown.

Approximate the area of the region using the rectangles of equal width shown.

Precalculus with Limits: A Graphing Approach

Precalculus with Limits: A Graphing Approach

7th Edition

ISBN: 9781305071711

Author: Ron Larson

Publisher: Brooks/Cole

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Question

Chapter 11, Problem 96RE

To determine

Approximate the area of the region using the rectangles of equal width shown.

Expert Solution & Answer

Answer to Problem 96RE

The area under the region is 3.53 square units.

Explanation of Solution

Given:

The given function:

$f(x)=4−x2$

Precalculus with Limits: A Graphing Approach, Chapter 11, Problem 96RE

Here length of the interval along x -axis is 3 units and there are six rectangles, the width of the rectangle is $14$

Height of each rectangle can be obtained by evaluating $f$ at the right end point of each interval

The six intervals are as follows:

$(0,14)⋅(14,12),(12,34)and(34,1)$

The right end point of each interval is $14i$ for $i=1,2,3,4.$

Therefore the sum of areas of four rectangles is

$∑i=14f(14i)(14)=∑i=14(4−(14i)2)(14)=∑i=14(1−164i2)=∑i=141−164∑i4i2$

Use properties of summation $∑i=1∞i=n(n+1)(2n+1)6$ and $∑i=1nc=nc$

$∑i=14f(14i)(14)=4−164(4×5×96)=4−180384=3.53$

Therefore, the area under the region is 3.53 square units.

Chapter 11, Problem 95RE

Chapter 11, Problem 97RE

Chapter 11 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - Prob. 15E Ch. 11.1 - Prob. 16E Ch. 11.1 - Prob. 17E Ch. 11.1 - Prob. 18E Ch. 11.1 - Prob. 19E Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Prob. 35E Ch. 11.1 - Prob. 36E Ch. 11.1 - Prob. 37E Ch. 11.1 - Prob. 38E Ch. 11.1 - Prob. 39E Ch. 11.1 - Prob. 40E Ch. 11.1 - Prob. 41E Ch. 11.1 - Prob. 42E Ch. 11.1 - Prob. 43E Ch. 11.1 - Prob. 44E Ch. 11.1 - Prob. 45E Ch. 11.1 - Prob. 46E Ch. 11.1 - Prob. 47E Ch. 11.1 - Prob. 48E Ch. 11.1 - Prob. 49E Ch. 11.1 - Prob. 50E Ch. 11.1 - Prob. 51E Ch. 11.1 - Prob. 52E Ch. 11.1 - Prob. 53E Ch. 11.1 - Prob. 54E Ch. 11.1 - Prob. 55E Ch. 11.1 - Prob. 56E Ch. 11.1 - Prob. 57E Ch. 11.1 - Prob. 58E Ch. 11.1 - 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