1) Consider the region bounded by y=e",y=2,x=0. a. Find the area of this region. Evaluate this integral by hand, giving your answer in exact form. b. Find the volume of the solid formed if this region is revolved about the x-axis. Evaluate this integral by hand, giving your answer in exact form. c. SET UP AN INTEGRAL to find the volume of the solid formed if this region is revolved about the line y=2. d. SET UP AN INTEGRAL to find the volume of the solid formed if this region is revolved about the y-axis. e. SET UP AN INTEGRAL to find the volume of the solid formed if this region is revolved about the linex=4. f. Let the region described above be the BASE of a solid, whose cross-sections perpendicular to the x-axis are EQUILATERAL TRIANGLES. SET UP AN INTEGRAL TO find the volume of this solid.

1) Consider the region bounded by y=e",y=2,x=0. a. Find the area of this region. Evaluate this integral by hand, giving your answer in exact form. b. Find the volume of the solid formed if this region is revolved about the x-axis. Evaluate this integral by hand, giving your answer in exact form. c. SET UP AN INTEGRAL to find the volume of the solid formed if this region is revolved about the line y=2. d. SET UP AN INTEGRAL to find the volume of the solid formed if this region is revolved about the y-axis. e. SET UP AN INTEGRAL to find the volume of the solid formed if this region is revolved about the linex=4. f. Let the region described above be the BASE of a solid, whose cross-sections perpendicular to the x-axis are EQUILATERAL TRIANGLES. SET UP AN INTEGRAL TO find the volume of this solid.

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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