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Question 2 Consider the region R in the xy-plane bounded by y = e, y = 1 and x = 1. (a) Set up, but do not evaluate, an integral that calculates the area of R. (b) Set up, but do not evaluate, an integral that gives the volume of the solid with base R and cross sections perpendicular to the x-axis that are squares. (c) Set up, but do not evaluate, an integral that gives the volume of the solid with base R and cross sections perpendicular to the x-axis that are equilateral triangles. (d) Set up, but do not evaluate, an integral that gives the volume of the solid with base R and cross sections perpendicular to the x-axis that are semicircles. (e) Set up, but do not evaluate, an integral that calculates the volume of the region obtained by rotating R about the x-axis. (f) Set up, but do not evaluate, an integral that calculates the volume of the region obtained by rotating R about the y-axis.

Question 2 Consider the region R in the xy-plane bounded by y = e, y = 1 and x = 1. (a) Set up, but do not evaluate, an integral that calculates the area of R. (b) Set up, but do not evaluate, an integral that gives the volume of the solid with base R and cross sections perpendicular to the x-axis that are squares. (c) Set up, but do not evaluate, an integral that gives the volume of the solid with base R and cross sections perpendicular to the x-axis that are equilateral triangles. (d) Set up, but do not evaluate, an integral that gives the volume of the solid with base R and cross sections perpendicular to the x-axis that are semicircles. (e) Set up, but do not evaluate, an integral that calculates the volume of the region obtained by rotating R about the x-axis. (f) Set up, but do not evaluate, an integral that calculates the volume of the region obtained by rotating R about the y-axis.

Advanced Engineering Mathematics
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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Question 1 Use a definite integral to calculate the volume of a pyramid with square base of length 3 m and height 11 m. Be sure to first find the approximate volume of a slice as we've been doing in class, add up the volumes of all the slices, and take the limit to obtain this integral. Question 2 Consider the region R in the xy-plane bounded by y = e*, y = 1 and x = 1. (a) Set up, but do not evaluate, an integral that calculates the area of R. (b) Set up, but do not evaluate, an integral that gives the volume of the solid with base R and cross sections perpendicular to the x-axis that are squares. (c) Set up, but do not evaluate, an integral that gives the volume of the solid with base R and cross sections perpendicular to the x-axis that are equilateral triangles. (d) Set up, but do not evaluate, an integral that gives the volume of the solid with base R and cross sections perpendicular to the x-axis that are semicircles. (e) Set up, but do not evaluate, an integral that calculates the volume of the region obtained by rotating R about the x-axis. (f) Set up, but do not evaluate, an integral that calculates the volume of the region obtained by rotating R about the y-axis.
Transcribed Image Text:Question 1 Use a definite integral to calculate the volume of a pyramid with square base of length 3 m and height 11 m. Be sure to first find the approximate volume of a slice as we've been doing in class, add up the volumes of all the slices, and take the limit to obtain this integral. Question 2 Consider the region R in the xy-plane bounded by y = e*, y = 1 and x = 1. (a) Set up, but do not evaluate, an integral that calculates the area of R. (b) Set up, but do not evaluate, an integral that gives the volume of the solid with base R and cross sections perpendicular to the x-axis that are squares. (c) Set up, but do not evaluate, an integral that gives the volume of the solid with base R and cross sections perpendicular to the x-axis that are equilateral triangles. (d) Set up, but do not evaluate, an integral that gives the volume of the solid with base R and cross sections perpendicular to the x-axis that are semicircles. (e) Set up, but do not evaluate, an integral that calculates the volume of the region obtained by rotating R about the x-axis. (f) Set up, but do not evaluate, an integral that calculates the volume of the region obtained by rotating R about the y-axis.
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