Q12. Let R be the region that lies between the curve y = (a) and the x-axis on the interval [2, ∞). x2/3 The graph of y= is given here: 5 x2/3 The area of R corresponds to the improper integral Determine whether this improper integral converges or diverges. If it converges, find its exact value. Your answer must be well-justified. 5 x²/3 dx. (b) |* : Let S be the solid obtained by revolving R about the x-axis. Give an expression for the approximate volume V(x) of the thin slice of S that lies between x and x + Ax, where its thickness Ax is assumed to be small. (c) Give an improper integral that computes the volume of S and determine whether it converges or diverges. If it converges, find the exact volume of S. Your answer must be well-justified and use appropriate mathematical notation.
Q12. Let R be the region that lies between the curve y = (a) and the x-axis on the interval [2, ∞). x2/3 The graph of y= is given here: 5 x2/3 The area of R corresponds to the improper integral Determine whether this improper integral converges or diverges. If it converges, find its exact value. Your answer must be well-justified. 5 x²/3 dx. (b) |* : Let S be the solid obtained by revolving R about the x-axis. Give an expression for the approximate volume V(x) of the thin slice of S that lies between x and x + Ax, where its thickness Ax is assumed to be small. (c) Give an improper integral that computes the volume of S and determine whether it converges or diverges. If it converges, find the exact volume of S. Your answer must be well-justified and use appropriate mathematical notation.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please send solution Q12 part b
Transcribed Image Text:Q12. Let R be the region that lies between the curve y =
r2/3
and the x-axis on the interval (2, 0).
The graph of y =
x2/3
is given here:
(a)
The area of R corresponds to the improper integral
d.x.
x2/3
Determine whether this improper integral converges or diverges. If it converges, find its exact value.
Your answer must be well-justified.
* Let S be the solid obtained by revolving R about the x-axis. Give an expression for the
(b) | * :
approximate volume V(x) of the thin slice of S that lies between x and x+Ax, where its thickness
Ax is assumed to be small.
(c)
converges or diverges. If it converges, find the exact volume of S. Your answer must be well-justified
and use appropriate mathematical notation.
Give an improper integral that computes the volume of S and determine whether it
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