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Solved: Volumes of solids Find the volume of the following

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

Solution for problem 43E 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 43E

Volumes of solids

Find the volume of the following solids.

The region bounded by y = x/(x + 1), the x-axis, and x = 4 is revolved about the x-axis.

Step-by-Step Solution:

Problem 43E

 Volume of  solids . Find the volume of the following solids.

The region  bounded by y =  , the x -axis , and x=4 is revolved about the x-axis.

Answer;

Step 1

           In this problem we need to find the volume of the solid founded by  the region  bounded by y =   , the x -axis  , and x =4  is revolved about the x-axis.

In order to find the volume, we will be using the following condition.

        If f is a function such that for all  in the interval , then the volume of the solid generated by revolving, around the x axis, the region bounded by the graph of , the x axis (y = 0) and the vertical lines andis given by the integral

                                        Volume

       [ The radius  for  our  cylinder would be the function f(x) and the height of our cylinder would be the  distance of each disk ;dx

                    The volume of each slice would be

                                                  V =  dx

           Adding the volumes of the disks  with infinitely small dx would give us to the formula              

                                                    V =  dx

                              Here , f(x)  =  radius

                                       dx = height of each disk

                                  [a , b]  = total height of a cylinder . ]  

Proper fraction definition ; In a rational fraction  , if the degree of f(x) < the degree of g(x) , then the rational fraction is called a proper fraction.

         The sum of two proper fractions is a proper fraction.

                                  Example;

Partial fractions Depending upon the nature of factors of Denominator ;

  When the denominator has repeated  linear factors

                           A repeated linear factor  of denominator corresponds partial fractions of the form ;

                  =  + ++......................+

Where A, B, C,............N are constants which can be determined by equating the numerator of L.H.Sto the numerator of R.H.S , and substituting x = a, we get N.

                 Example;

Improper fraction definition ; In a rational fraction  , if the degree of f(x)  the degree of g(x) , then the rational fraction is called a improper fraction.

          If an improper rational fraction   is given for splitting into partial fractions, we first divide f(x) with g(x) till we obtain a remainder R(x) of lower degree than g(x).

          First we express the fraction in the form   = quotient

          Then we resolve  the final proper fractions into partial fractions.

 

Step 2 of 4

Chapter 7.4, Problem 43E is Solved
Step 3 of 4

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

The answer to “Volumes of solids Find the volume of the following solids.The region bounded by y = x/(x + 1), the x-axis, and x = 4 is revolved about the x-axis.” is broken down into a number of easy to follow steps, and 29 words. The full step-by-step solution to problem: 43E from chapter: 7.4 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 43E from 7.4 chapter was answered, more than 331 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This full solution covers the following key subjects: axis, solids, revolved, region, Find. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567.

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Solved: Volumes of solids Find the volume of the following