a) Sketch the infinite region bounded by f(x) = ! and the r-axis, for r > 1. b) Set up and evaluate an improper integral to find the area of the region. c) Sketch the solid of revolution obtained by rotating the region about the z-axis. d) Set up and evaluate an integral to find the volume of this solid. e) Set up and evaluate an integral to find the surface area of this solid (using the formula below). f) What is strange about yours results to parts b), d), and e)? If a region is bounded by f(z), the z-axis, z = a, and z = b, and is rotated about the r-axis, this solid's surface is given by the formula f(x)/1+ 2. Use the arc length formula to find the circumference of a circle of radius r.
a) Sketch the infinite region bounded by f(x) = ! and the r-axis, for r > 1. b) Set up and evaluate an improper integral to find the area of the region. c) Sketch the solid of revolution obtained by rotating the region about the z-axis. d) Set up and evaluate an integral to find the volume of this solid. e) Set up and evaluate an integral to find the surface area of this solid (using the formula below). f) What is strange about yours results to parts b), d), and e)? If a region is bounded by f(z), the z-axis, z = a, and z = b, and is rotated about the r-axis, this solid's surface is given by the formula f(x)/1+ 2. Use the arc length formula to find the circumference of a circle of radius r.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 41E: Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed...
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ANSWER PARTS D,E, F, AND NUMBER 2 ONLY.
Transcribed Image Text:a) Sketch the infinite region bounded by f(x) = ! and the r-axis, for r > 1.
b) Set up and evaluate an improper integral to find the area of the region.
c) Sketch the solid of revolution obtained by rotating the region about the z-axis.
d) Set up and evaluate an integral to find the volume of this solid.
e) Set up and evaluate an integral to find the surface area of this solid (using the formula below).
f) What is strange about yours results to parts b), d), and e)?
If a region is bounded by f(z), the z-axis, z = a, and z = b, and is rotated about the r-axis, this
solid's surface is given by the formula
f(x)/1+
2.
Use the arc length formula to find the circumference of a circle of radius r.
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