y = sin(x), y = 0, x=0, x= π Exercise (a) the volume of the solid formed by revolving the region about the x-axis Step 1 The region is bounded by the graphs of the equations y = sin x, y = 0, x = 0, and x = #. AX For the representative rectangle, the radius of the solid of revolution is R(x) = sin x Therefore, According to the disk method, the volume of the solid of revolution, when the area is revolved about the x axis is = = [° [R(x)] = • V = *f* Hence, Step 2 Use the half angle identity for sin² x. sin²x = (sin(x)) y=sin(x) V = R 2 *S* (² =[x - sin 2x] - -| sin(x) R(X) dx. dx. )- dx - (0)] The volume of the solid of revolution is V=
y = sin(x), y = 0, x=0, x= π Exercise (a) the volume of the solid formed by revolving the region about the x-axis Step 1 The region is bounded by the graphs of the equations y = sin x, y = 0, x = 0, and x = #. AX For the representative rectangle, the radius of the solid of revolution is R(x) = sin x Therefore, According to the disk method, the volume of the solid of revolution, when the area is revolved about the x axis is = = [° [R(x)] = • V = *f* Hence, Step 2 Use the half angle identity for sin² x. sin²x = (sin(x)) y=sin(x) V = R 2 *S* (² =[x - sin 2x] - -| sin(x) R(X) dx. dx. )- dx - (0)] The volume of the solid of revolution is V=
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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![y = sin(x), y = 0, x = 0, x = π
Exercise (a)
the volume of the solid formed by revolving the region about the x-axis
Step 1
The region is bounded by the graphs of the equations
y sin x, y = 0, x = 0, and x = *.
For the representative rectangle, the radius of the solid of revolution is
R(x) = sin x
V = T
Therefore,
According to the disk method, the volume of the solid of revolution, when the area is revolved about the x axis is
12✔
= = [ D [R(X)] ²
Hence,
V = x 6² (sin(x))
Step 2
Use the half angle identity for sin² x.
sin²x =
V = π
1
=
y=sin(x)
sin 2x1
--x-2x
2
=(x-
=
¹0
2
R(X)
sin(x)
dx.
dx.
dx
- (0)]
The volume of the solid of revolution is V =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0fdef185-de8b-42f5-933e-8018dcf36541%2Ff036d3e0-edc0-456a-a9a9-9886fd728337%2F8k2h14m_processed.png&w=3840&q=75)
Transcribed Image Text:y = sin(x), y = 0, x = 0, x = π
Exercise (a)
the volume of the solid formed by revolving the region about the x-axis
Step 1
The region is bounded by the graphs of the equations
y sin x, y = 0, x = 0, and x = *.
For the representative rectangle, the radius of the solid of revolution is
R(x) = sin x
V = T
Therefore,
According to the disk method, the volume of the solid of revolution, when the area is revolved about the x axis is
12✔
= = [ D [R(X)] ²
Hence,
V = x 6² (sin(x))
Step 2
Use the half angle identity for sin² x.
sin²x =
V = π
1
=
y=sin(x)
sin 2x1
--x-2x
2
=(x-
=
¹0
2
R(X)
sin(x)
dx.
dx.
dx
- (0)]
The volume of the solid of revolution is V =
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