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189. [T] x = 4 from y=0 to y = 2 190. [T] x = ln(y) on y = to y = e For the following exercises, find the surface area of the solid generated when the following curves revolve around the x-axis. Write your answer as an exact number. 191. y = √x from x=2 to x = 6 192. y = x³ from x=0 to x = 1 193. y = 7x from x = -1 to x = 1 194. [T] y = from x 글 x = 1 tox=3 195. y = 14-x² from x = 0 tox=2 196. y = 14-x² from x= -1 to x = 1 197. y = 5x from x = 1 tox=5 198. [T] y = tan x from x= -4tox=4 For the following exercises, find the surface area of the solid generated when the following curves revolve around the y-axis. Write your result as an exact number. 199. y=x² from x=0 tox=2

189. [T] x = 4 from y=0 to y = 2 190. [T] x = ln(y) on y = to y = e For the following exercises, find the surface area of the solid generated when the following curves revolve around the x-axis. Write your answer as an exact number. 191. y = √x from x=2 to x = 6 192. y = x³ from x=0 to x = 1 193. y = 7x from x = -1 to x = 1 194. [T] y = from x 글 x = 1 tox=3 195. y = 14-x² from x = 0 tox=2 196. y = 14-x² from x= -1 to x = 1 197. y = 5x from x = 1 tox=5 198. [T] y = tan x from x= -4tox=4 For the following exercises, find the surface area of the solid generated when the following curves revolve around the y-axis. Write your result as an exact number. 199. y=x² from x=0 tox=2

Calculus: Early Transcendentals
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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189. [T] x 4" from y = 0 to y = 2 = 190. [T] x = ln(y) on y = ½ to y = e For the following exercises, find the surface area of the solid generated when the following curves revolve around the x-axis. Write your answer as an number. exact 191. y = √x from x = 2 to x = 6 3 192. y = x³ from x = 0 to x = 1 193. y = 7x from x = -1 to x = 1 =1/12 X 194. [T] y = from x = 1 to x = 3 2 195. y = √4x² from x = 0 to x = 2 196. y = √4x² from x = −1 to x = 1 197. y = 5x from x = 1 to x = 5 198. [T] y tan x from x = − -to x = 4 For the following exercises, find the surface area of the solid generated when the following curves revolve around the y-axis. Write your result as an exact number. 199. y = x² from x = 0 to x = 2 2 1.0 207. The base of a lamp is constructed by revolving a quarter circle y = √2x-x² around the y-axis from x = 1 to x=2, as seen here. Create an integral for the surface area of this curve and compute it. -2 y =₁2x-x² у 0.5 0.0 2 Z 1 Page < 0 0 2 X 1 of 5 2 208. A light bulb is a sphere with radius 1/2 in. with the bottom sliced off to fit exactly onto a cylinder of radius 1/4 in. and length 1/3 in., as seen here. The sphere is cut off at the bottom to fit exactly onto the cylinder, so the radius of the cut is 1/4 in. Find the surface area (not including the top or bottom of the cylinder). 209. [T] A lampshade is constructed by rotating y = 1/x around the x-axis from y = 1 to y = 2, as seen here. Determine how much material you would need to construct this lampshade that is, the surface area-accurate to four ZOOM + I
Transcribed Image Text:189. [T] x 4" from y = 0 to y = 2 = 190. [T] x = ln(y) on y = ½ to y = e For the following exercises, find the surface area of the solid generated when the following curves revolve around the x-axis. Write your answer as an number. exact 191. y = √x from x = 2 to x = 6 3 192. y = x³ from x = 0 to x = 1 193. y = 7x from x = -1 to x = 1 =1/12 X 194. [T] y = from x = 1 to x = 3 2 195. y = √4x² from x = 0 to x = 2 196. y = √4x² from x = −1 to x = 1 197. y = 5x from x = 1 to x = 5 198. [T] y tan x from x = − -to x = 4 For the following exercises, find the surface area of the solid generated when the following curves revolve around the y-axis. Write your result as an exact number. 199. y = x² from x = 0 to x = 2 2 1.0 207. The base of a lamp is constructed by revolving a quarter circle y = √2x-x² around the y-axis from x = 1 to x=2, as seen here. Create an integral for the surface area of this curve and compute it. -2 y =₁2x-x² у 0.5 0.0 2 Z 1 Page < 0 0 2 X 1 of 5 2 208. A light bulb is a sphere with radius 1/2 in. with the bottom sliced off to fit exactly onto a cylinder of radius 1/4 in. and length 1/3 in., as seen here. The sphere is cut off at the bottom to fit exactly onto the cylinder, so the radius of the cut is 1/4 in. Find the surface area (not including the top or bottom of the cylinder). 209. [T] A lampshade is constructed by rotating y = 1/x around the x-axis from y = 1 to y = 2, as seen here. Determine how much material you would need to construct this lampshade that is, the surface area-accurate to four ZOOM + I
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