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Solved: Area between curves Let R be the region bounded by

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

Solution for problem 57E Chapter 7.7

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 57E

Problem 57E

Area between curves Let R be the region bounded by the graphs of y = e−ax and y =e−bxfor x ≥ 0, where a > b > 0. Find the area of R.

Step-by-Step Solution:

Problem 57E

Area between curves Let R be the region bounded by the graphs of y = and y =for x ≥ 0, where a > b > 0. Find the area of R.

Answer;

   

       Step 1;

           

                Let R be the region bounded by the graph of  y = and  y =for x ≥ 0, where a > b > 0.

             Now , we have to find out the area between the curves.

   

        Given  a > b > 0, in the interval [0, infinity), the graph of e−bx will always be above the graph of e−ax. So the setup of the area integral is ∫(e−bx − e−ax)dx from 0 to ∞. This can be rewritten as the difference of two integrals:

                         = ………(1)

                     Consider ,

                                        Put -bx = t , then -b dx = dt

                                                                        dx = dt

                               

                              Therefore,  = (dt)

                                                              = dt

                                               

                                                               =  

 

                                                               = ………..(2)

Step 2 of 3

Chapter 7.7, Problem 57E is Solved
Step 3 of 3

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. Since the solution to 57E from 7.7 chapter was answered, more than 315 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 57E from chapter: 7.7 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This full solution covers the following key subjects: area, Find, bxfor, curves, bounded. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The answer to “Area between curves Let R be the region bounded by the graphs of y = e?ax and y =e?bxfor x ? 0, where a > b > 0. Find the area of R.” is broken down into a number of easy to follow steps, and 33 words. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1.

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Solved: Area between curves Let R be the region bounded by