1. Let fand g be functions given by f(x)=- enclosed by the graphs off and g. x² +2 and g(x) = -x +2. Let R be the region in the first quadrant 2 f(x) == a. Graph the fand g on the same axes and indicate region R. b. Find the area of R. A = $((-2+²+2)-(-x+2) 3 dx 3 c. Find the value of z so that x = z cuts the solid R into two parts of equal area. d. Find the volume of the solid generated when R is revolved around the x-axis. = 5 e. The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are semicircles with diameters extending from f(x) to g(x). Find the volume of the solid. IT f. Find the volume of the solid generated when R is revolved around the y-axis. 1 30 3 g. Find the volume of the solid generated when R is revolved around the line y = -1. g(x)= 0-2 ²2=-x 2x x ²0 'x (x) x-21₁ =
1. Let fand g be functions given by f(x)=- enclosed by the graphs off and g. x² +2 and g(x) = -x +2. Let R be the region in the first quadrant 2 f(x) == a. Graph the fand g on the same axes and indicate region R. b. Find the area of R. A = $((-2+²+2)-(-x+2) 3 dx 3 c. Find the value of z so that x = z cuts the solid R into two parts of equal area. d. Find the volume of the solid generated when R is revolved around the x-axis. = 5 e. The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are semicircles with diameters extending from f(x) to g(x). Find the volume of the solid. IT f. Find the volume of the solid generated when R is revolved around the y-axis. 1 30 3 g. Find the volume of the solid generated when R is revolved around the line y = -1. g(x)= 0-2 ²2=-x 2x x ²0 'x (x) x-21₁ =
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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![W! WHAT A WORKSHEET ON AREA/VOLUME!
COMPLETE YOUR WORK ON A SEPARATE SHEET. BE SURE TO DRAW EACH REGION.
1
1. Let fand g be functions given by f(x)=-=-x² +2 and g(x) = -x + 2. Let R be the region in the first quadrant
2
enclosed by the graphs off and g.
a. Graph the fand g on the same axes and indicate region R.
A =
S((--/+ ²+2)-(-x+2) ]dx
b. Find the area of R.
- ²/3
Z=1
c. Find the value of z so that x = z cuts the solid R into two parts of equal area.
d. Find the volume of the solid generated when R is revolved around the x-axis. V=
f. Find the volume of the solid generated when R is revolved around the y-axis. I 30
3
g. Find the volume of the solid generated when R is revolved around the line y = -1.
-2
f(x) = =√x ² + ²
2-1ײ+
24
g(x)==x+2
0=-x+2
42
- 1/21/²²/2 = -x ² + 2
x²=9=2x-4
k. Find the volume of the solid generated when R is revolved around the line x = -2.
1. Find the volume of the solid generated when R is revolved around the line y = 3
x ²2 x 210
x (x
x=0x=2
5
IT
e. The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are semicircles
with diameters extending from f(x) to g(x). Find the volume of the solid.
h. Find the volume of the solid generated when R is revolved around the line x = 2.
i. The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are rectangles
with height 5. Find the volume of this solid.
j. The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are squares. Find
the volume of this solid.
m. The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are rectangles
with height twice its width. Find the volume of this solid.
n. The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are isosceles right
triangles with their hypotenuse on the base. Find the volume of this solid.
o. The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are equilateral
triangles. Find the volume of the solid.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ebf45e9-5220-4347-b924-faecd2ff7a3c%2F6ab059eb-ebce-4cd7-9e5f-56ccdd3b5402%2Fb8jfrvw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:W! WHAT A WORKSHEET ON AREA/VOLUME!
COMPLETE YOUR WORK ON A SEPARATE SHEET. BE SURE TO DRAW EACH REGION.
1
1. Let fand g be functions given by f(x)=-=-x² +2 and g(x) = -x + 2. Let R be the region in the first quadrant
2
enclosed by the graphs off and g.
a. Graph the fand g on the same axes and indicate region R.
A =
S((--/+ ²+2)-(-x+2) ]dx
b. Find the area of R.
- ²/3
Z=1
c. Find the value of z so that x = z cuts the solid R into two parts of equal area.
d. Find the volume of the solid generated when R is revolved around the x-axis. V=
f. Find the volume of the solid generated when R is revolved around the y-axis. I 30
3
g. Find the volume of the solid generated when R is revolved around the line y = -1.
-2
f(x) = =√x ² + ²
2-1ײ+
24
g(x)==x+2
0=-x+2
42
- 1/21/²²/2 = -x ² + 2
x²=9=2x-4
k. Find the volume of the solid generated when R is revolved around the line x = -2.
1. Find the volume of the solid generated when R is revolved around the line y = 3
x ²2 x 210
x (x
x=0x=2
5
IT
e. The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are semicircles
with diameters extending from f(x) to g(x). Find the volume of the solid.
h. Find the volume of the solid generated when R is revolved around the line x = 2.
i. The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are rectangles
with height 5. Find the volume of this solid.
j. The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are squares. Find
the volume of this solid.
m. The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are rectangles
with height twice its width. Find the volume of this solid.
n. The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are isosceles right
triangles with their hypotenuse on the base. Find the volume of this solid.
o. The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are equilateral
triangles. Find the volume of the solid.
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