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Solution: Areas of regions Find the area of the following

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 40E Chapter 7.4

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 40E

Areas of regions

Find the area of the following regions. In each case, graph the relevant functions and show the region in question.

The region bounded by the curves y = 1/x, y = x/(3x +4), and the line x =10.

Step-by-Step Solution:

Problem 40E

Find the area of the following regions. In each case, graph the relevant functions and show the region in question.

The region bounded by the curves y = 1/x, y = x/(3x +4), and the line x =10.Solution:-Step 1The graph of

The graph of y = isThe graph of y=10

The graph of the region bounded by these curves isStep 2We must find the point of intersection of different curves with each other and X-axis to find the region bounded by them.

Point of intersection for curves are calculated as follows,1.  and y=10  For  2. y = and    Equating both the functions, we getEither 3. Also, y =  passes through the origin.Step 3From

The bounded region is between . Here y= 10 is above is below ,so area is calculated as follows     =   =   =   =    =    =       Putting the limits, we get  = = 0.998

This is the area bounded by y=10 and y=From x= to , the area bounded is between and  y=. Here is above and  y=is below , so area is calculated as follows,

         =          =          =          =          =          =          =  3.688-1.3+0.5839          = 2.972

Total region bounded by these curves is = 0.998+2.972= 3.96

The region bounded by the curves y = 1/x, y = x/(3x +4), and the line x =10 is  3.96.    

 

Step 3 of 3

Chapter 7.4, Problem 40E is Solved
Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The full step-by-step solution to problem: 40E from chapter: 7.4 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The answer to “Areas of regions Find the area of the following regions. In each case, graph the relevant functions and show the region in question.The region bounded by the curves y = 1/x, y = x/(3x +4), and the line x =10.” is broken down into a number of easy to follow steps, and 40 words. Since the solution to 40E from 7.4 chapter was answered, more than 312 students have viewed the full step-by-step answer. This full solution covers the following key subjects: region, regions, graph, Case, curves. This expansive textbook survival guide covers 85 chapters, and 5218 solutions.

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