Name C Page 1 > - ZOOM + Date Day #66 Homework Class of 4 Let R be the region bounded by the graphs of y = ln x and the line y=x-2 as shown below. Though you may use a calculator, show the integral that you found to arrive at your answer. 1. Find the volume of the solid whose base is region R that is formed by cross sections that are semi-circles that are perpendicular to the x-axis. 2. Find the volume of the solid whose base is region R that is formed by cross sections that are squares that are perpendicular to the x-axis. Let f and g be the functions given by f(x) = ½-½ + sin(xx) and g(x) = 4¯*. Let R be the region in the first quadrant enclosed by the y-axis and the graphs off and g, and let S be the region in the first quadrant enclosed by the graphs off and g shown to the right. Though you may use a calculator, show the integral that you found to arrive at your answer. 3. Find the volume of the solid whose base is the cross section area of region S and is formed by squares that are perpendicular to the x-axis. = x) 4. Find the volume of the solid whose base is the cross section area of region S and is formed by equilateral triangles that are perpendicular to the x-axis. AP* Calculus AB Page 602 Let ƒ and g be the functions given by f(x) = 2x(1-x)and g(x) = 3(x-1)√x for 0≤x≤1. The graphs of ƒ --------- AP* Calculus AB Page 2 > of 4 - ZOOM + Page 602 --------- Let f and g be the functions given by f(x) = 2x(1-x)and g(x) = 3(x−1)√x for 0≤x≤1. The graphs of ƒ and g are shown in the figure to the right. Though you may use a calculator, show the integral that you found to arrive at your answer. 5. Find the volume of the solid whose base is the cross section of the region bounded by the graphs off and g and is formed by squares that are perpendicular to the x-axis. y=f(x) y = g(x) 6. Find the volume of the solid whose base is the cross section of the region bounded by the graphs of f and g and is formed by semi-circles that are perpendicular to the x-axis. 7. Find the volume of the solid whose base is the cross section of the region bounded by the graphs of f and g and is formed by equilateral triangles that are perpendicular to the x-axis. 8. Find the volume of the solid whose base is the cross section of the region bounded by the graphs of f and g and is formed by right isosceles triangles that are perpendicular to the x-axis. AP* Calculus AB Page 603 Drag from top and touch the back button to exit full screen.
Name C Page 1 > - ZOOM + Date Day #66 Homework Class of 4 Let R be the region bounded by the graphs of y = ln x and the line y=x-2 as shown below. Though you may use a calculator, show the integral that you found to arrive at your answer. 1. Find the volume of the solid whose base is region R that is formed by cross sections that are semi-circles that are perpendicular to the x-axis. 2. Find the volume of the solid whose base is region R that is formed by cross sections that are squares that are perpendicular to the x-axis. Let f and g be the functions given by f(x) = ½-½ + sin(xx) and g(x) = 4¯*. Let R be the region in the first quadrant enclosed by the y-axis and the graphs off and g, and let S be the region in the first quadrant enclosed by the graphs off and g shown to the right. Though you may use a calculator, show the integral that you found to arrive at your answer. 3. Find the volume of the solid whose base is the cross section area of region S and is formed by squares that are perpendicular to the x-axis. = x) 4. Find the volume of the solid whose base is the cross section area of region S and is formed by equilateral triangles that are perpendicular to the x-axis. AP* Calculus AB Page 602 Let ƒ and g be the functions given by f(x) = 2x(1-x)and g(x) = 3(x-1)√x for 0≤x≤1. The graphs of ƒ --------- AP* Calculus AB Page 2 > of 4 - ZOOM + Page 602 --------- Let f and g be the functions given by f(x) = 2x(1-x)and g(x) = 3(x−1)√x for 0≤x≤1. The graphs of ƒ and g are shown in the figure to the right. Though you may use a calculator, show the integral that you found to arrive at your answer. 5. Find the volume of the solid whose base is the cross section of the region bounded by the graphs off and g and is formed by squares that are perpendicular to the x-axis. y=f(x) y = g(x) 6. Find the volume of the solid whose base is the cross section of the region bounded by the graphs of f and g and is formed by semi-circles that are perpendicular to the x-axis. 7. Find the volume of the solid whose base is the cross section of the region bounded by the graphs of f and g and is formed by equilateral triangles that are perpendicular to the x-axis. 8. Find the volume of the solid whose base is the cross section of the region bounded by the graphs of f and g and is formed by right isosceles triangles that are perpendicular to the x-axis. AP* Calculus AB Page 603 Drag from top and touch the back button to exit full screen.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.3: Volume And Average Value
Problem 22E
Related questions
Question
Transcribed Image Text:Name
C
Page
1
>
-
ZOOM
+
Date
Day #66 Homework
Class
of 4
Let R be the region bounded by the graphs of y = ln x and the line y=x-2 as shown below. Though you
may use a calculator, show the integral that you found to arrive at your answer.
1. Find the volume of the solid whose base is region R that is formed by cross
sections that are semi-circles that are perpendicular to the x-axis.
2. Find the volume of the solid whose base is region R that is formed by cross sections that are squares
that are perpendicular to the x-axis.
Let f and g be the functions given by f(x) = ½-½ + sin(xx) and g(x) = 4¯*. Let R be the region in the first
quadrant enclosed by the y-axis and the graphs off and g, and let S be the region in the first quadrant
enclosed by the graphs off and g shown to the right. Though you may use a calculator, show the integral
that you found to arrive at your answer.
3. Find the volume of the solid whose base is the cross section area of
region S and is formed by squares that are perpendicular to the x-axis.
= x)
4. Find the volume of the solid whose base is the cross section area of region S and is formed by
equilateral triangles that are perpendicular to the x-axis.
AP* Calculus AB
Page 602
Let ƒ and g be the functions given by f(x) = 2x(1-x)and g(x) = 3(x-1)√x for 0≤x≤1. The graphs of ƒ
---------
Transcribed Image Text:AP* Calculus AB
Page
2
>
of 4
-
ZOOM
+
Page 602
---------
Let f and g be the functions given by f(x) = 2x(1-x)and g(x) = 3(x−1)√x for 0≤x≤1. The graphs of ƒ
and g are shown in the figure to the right. Though you may use a calculator, show the integral that you
found to arrive at your answer.
5. Find the volume of the solid whose base is the cross section of the
region bounded by the graphs off and g and is formed by squares that
are perpendicular to the x-axis.
y=f(x)
y = g(x)
6. Find the volume of the solid whose base is the cross section of the region bounded by the graphs of f
and g and is formed by semi-circles that are perpendicular to the x-axis.
7. Find the volume of the solid whose base is the cross section of the region bounded by the graphs of f
and g and is formed by equilateral triangles that are perpendicular to the x-axis.
8. Find the volume of the solid whose base is the cross section of the region bounded by the graphs of f
and g and is formed by right isosceles triangles that are perpendicular to the x-axis.
AP* Calculus AB
Page 603
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