×
Log in to StudySoup
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.7 - Problem 39e
Join StudySoup for FREE
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.7 - Problem 39e

Already have an account? Login here
×
Reset your password

Answer: Volumes with infinite integrands Find the volume

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

Solution for problem 39E Chapter 7.7

Calculus: Early Transcendentals | 1st Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

4 5 1 430 Reviews
22
2
Problem 39E

Volumes with infinite integrands Find the volume of the described solid of revolution or state that it does not exist.The region bounded by f(x) = (4 ? x)?1/3 and the x-axis on the interval [0, 4) is revolved about the y-axis.

Step-by-Step Solution:
Step 1 of 3

Problem 39EVolumes with infinite integrands Find the volume of the described solid of revolution or state that it does not exist.The region bounded by f(x) = (4 x)1/3 and the x-axis on the interval [0, 4) is revolved about the y-axis.Answer; Step-1; The shell method ; If R is the region under the curve y = f(x) on the interval [a , b] , then the volume of the solid obtained by revolving R about the y-axis is V = 2x f(x) dx.Step-2 Now , we have to find out the volume of the described solid under the region bounded by f(x) = and the x-axis on the interval [0 , 4) is revolved about the y-axis. Consider , y = f(x) = The visual representation of the interval is given below; | | axis of revolution\n | 1\/(4 - x)^(1\/3)\n | x-axis\n(axes not equally scaled) | Therefore , the volume of the described solid under the region bounded by f(x) = and the x-axis on the interval [0 , 4) is revolved about the y-axis is ; Volume (V) = 2x f(x) dx , since by the above formula. = 2x dx , since f(x) = . = dx , since = ……..(1) To evaluate this integral , let us use substitution method . Step-3 ; Consider , (4 -x) = , then = t , and 4 - = x If x = 0 , the lower limit of t = = = . If x = 4 , the upper limit of t = = = Differentiate both sides with respect to x , then ; ( 0 - 1) = 3 , since = n -dx = 3dt ……………(2)Step-4 ; From , (1) and (2) , the volume of the integral can be written as ; V = dx = , since from (2). = 2 (-3t)(4 - )dt = 6 dt , since f(x)dx = 6 = = 6(, since ( 5.0396842 - 2.0158737) 6(3.0238105) 56 .997485 Therefore , volume(V) = dx 56 .997485 Thus , the volume of the solid is ; .

Step 2 of 3

Chapter 7.7, Problem 39E 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. The full step-by-step solution to problem: 39E from chapter: 7.7 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. The answer to “Volumes with infinite integrands Find the volume of the described solid of revolution or state that it does not exist.The region bounded by f(x) = (4 ? x)?1/3 and the x-axis on the interval [0, 4) is revolved about the y-axis.” is broken down into a number of easy to follow steps, and 41 words. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Since the solution to 39E from 7.7 chapter was answered, more than 292 students have viewed the full step-by-step answer. This full solution covers the following key subjects: axis, interval, described, exist, Find. This expansive textbook survival guide covers 85 chapters, and 5218 solutions.

Other solutions

People also purchased

Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Answer: Volumes with infinite integrands Find the volume