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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 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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Question 1 and 2 please with neat handwriting

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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