1. Let S be the region bounded by the graphs of y = In x, y = 0, x = 2. (a) Sketch carefully this region. (b) Calculate the volume of the body obtained by rotating S around the y-axis by using the shell method. You will need to use integration by parts. State what u, dv, du, v are. Do not skip any details. (c) Calculate the volume of the body obtained by rotating S around the x-axis by using the disk method. You will need to use integration by parts. State what u, dv, du, v are. Do not skip any details.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. Let S be the region bounded by the graphs of y = In x, y = 0, x = 2.
(a) Sketch carefully this region.
(b) Calculate the volume of the body obtained by rotating S around the y-axis by using the
shell method.
You will need to use integration by parts. State what u, dv, du, v are. Do not skip any
details.
(c) Calculate the volume of the body obtained by rotating S around the x-axis by using the
disk method.
You will need to use integration by parts. State what u, dv, du, v are. Do not skip any
details.
Transcribed Image Text:1. Let S be the region bounded by the graphs of y = In x, y = 0, x = 2. (a) Sketch carefully this region. (b) Calculate the volume of the body obtained by rotating S around the y-axis by using the shell method. You will need to use integration by parts. State what u, dv, du, v are. Do not skip any details. (c) Calculate the volume of the body obtained by rotating S around the x-axis by using the disk method. You will need to use integration by parts. State what u, dv, du, v are. Do not skip any details.
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