AP Calculus AB
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03/25/22 Perkins AP Calculus AB Day 3 Section 7.2
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AP Calculus AB. Day 3 Section 7.2. Revolve this rectangle about the x-axis. Forms a Disk. Revolve this function about the x-axis. Disk Method (to find the volume of a solid of revolution). Horizontal Axis of revolution:. width. radius. Vertical Axis of revolution:. - PowerPoint PPT Presentation
Transcript of AP Calculus AB
04/19/23 Perkins
AP Calculus AB
Day 3Section 7.2
Revolve this rectangle about the x-axis.
x
f x
A B
Forms a Disk.
4
2
1i
i
V r x
disk circleV A x
x
2r x
f x
A B
Revolve this function about the x-axis.
f x
A B
2b
a
V f x dx
Disk Method (to find the volume of a solid of revolution) f x
A B 2b
a
V f x dx Horizontal Axis of revolution:
dx
f y
dy 2b
a
V f y dy
Vertical Axis of revolution:
radius width
1. Find the volume of the solid formed by revolving f(x) over about the x-axis.
2
0
sinV x dx
sinf x x
0,
2
1
-1
2 0 dx 0
sin x dx
0
cos x
cos cos0
1 1
2
2. Find the volume of the solid formed by revolving the region formed by f(x) and g(x) about y = 1.
1
22
1
1V x dx
22 and 1f x x g x
11
dx
22 1x
2
1
-2 2
Length of Rectangle:
2
1
-2 2
22 x1
21 x
1
2 4
1
1 2x x dx
13 52 1
3 5 1x x x
2 1 2 13 5 3 51 1
4 23 52
16
15
3. Find the volume of the solid formed by revolving the region formed by over about the y-axis.
4 2
0
V y dy
2y x
4
0
dy4
0
y dy
0,4y
4212 0y
8
4
3
2
1
-1
-2 2
y x
Perkins
AP Calculus AB
Day 3Section 7.2
Revolve this rectangle about the x-axis.
Revolve this function about the x-axis.
f x
A B
Disk Method (to find the volume of a solid of revolution) f x
A B
Horizontal Axis of revolution:
f yVertical Axis of revolution:
1. Find the volume of the solid formed by revolving f(x) over about the x-axis.
sinf x x
0,
2. Find the volume of the solid formed by revolving the region formed by f(x) and g(x) about y = 1.
22 and 1f x x g x
3. Find the volume of the solid formed by revolving the region formed by over about the y-axis.
2y x 0,4y
