Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 11.3, Problem 6E
To determine

Find the area of the curve y=x3 from x=0tox=4 and above the x − axis.

Expert Solution & Answer
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Answer to Problem 6E

The approximate area under the curve is 62 sq units.

Explanation of Solution

Given:

Find the area of the curve y=x3 from x=0tox=4 and above the x − axis.

Concept Used:

It is like sum of areas of 4 rectangles

The graph: y=x3

  Algebra 2, Chapter 11.3, Problem 6E

Calculation:

It is like sum of areas of 4 rectangles.

We find the area under the curve y=x3 from x=0tox=4 ,

According to the graph there are four rectangles.

First rectangle from x=0tox=1

Second rectangle from x=1tox=2

Third rectangle from x=2tox=3

Fourth rectangle from x=3tox=4

Width of each rectangle is 1 unit.

We use the midpoint of each rectangle.

Now find the height of each rectangle:

So height of first rectangle would be x=0.5(0.5)3=0.125

Height of second rectangle would be x=1.5(1.5)3=3.375

Height of third rectangle would be x=2.5(2.5)3=15.625

Height of fourth rectangle would be x=3.5(3.5)3=42.875

The area of 1st, 2nd, 3rd and 4th rectangles are : 0.125,3.375,15.625,42.875 sq unit.

So the approximate area under the curve = sum of all 4 rectangles

So the approximate area under the curve: 0.125+3.375+15.625+42.875=62 sq unit.

Thus, the approximate area under the curve is 62 sq units.

Chapter 11 Solutions

Algebra 2

Ch. 11.1 - Prob. 1CYUCh. 11.1 - Prob. 2CYUCh. 11.1 - Prob. 3CYUCh. 11.1 - Prob. 4CYUCh. 11.1 - Prob. 5CYUCh. 11.1 - Prob. 6CYUCh. 11.1 - Prob. 7CYUCh. 11.1 - Prob. 8CYUCh. 11.1 - Prob. 9CYUCh. 11.1 - Prob. 10CYUCh. 11.1 - Prob. 11CYUCh. 11.1 - Prob. 12CYUCh. 11.1 - Prob. 13CYUCh. 11.1 - Prob. 14CYUCh. 11.1 - Prob. 15CYUCh. 11.1 - Prob. 16CYUCh. 11.1 - Prob. 17CYUCh. 11.1 - Prob. 18CYUCh. 11.1 - Prob. 19CYUCh. 11.1 - Prob. 20CYUCh. 11.1 - Prob. 21PPSCh. 11.1 - Prob. 22PPSCh. 11.1 - Prob. 23PPSCh. 11.1 - Prob. 24PPSCh. 11.1 - Prob. 25PPSCh. 11.1 - Prob. 26PPSCh. 11.1 - Prob. 27PPSCh. 11.1 - Prob. 28PPSCh. 11.1 - Prob. 29PPSCh. 11.1 - Prob. 30PPSCh. 11.1 - Prob. 31PPSCh. 11.1 - Prob. 32PPSCh. 11.1 - Prob. 33PPSCh. 11.1 - Prob. 34PPSCh. 11.1 - Prob. 35PPSCh. 11.1 - Prob. 36PPSCh. 11.1 - Prob. 37PPSCh. 11.1 - Prob. 38PPSCh. 11.1 - Prob. 39PPSCh. 11.1 - Prob. 40PPSCh. 11.1 - Prob. 41PPSCh. 11.1 - Prob. 42PPSCh. 11.1 - Prob. 43PPSCh. 11.1 - Prob. 44PPSCh. 11.1 - Prob. 45PPSCh. 11.1 - Prob. 46PPSCh. 11.1 - 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ISBN:9781305657960
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Publisher:Cengage Learning
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ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
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ISBN:9780135163078
Author:Michael Sullivan
Publisher:PEARSON
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Introduction to Linear Algebra, Fifth Edition
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ISBN:9780980232776
Author:Gilbert Strang
Publisher:Wellesley-Cambridge Press
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ISBN:9780077836344
Author:Julie Miller, Donna Gerken
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY