C3-16-16.1, 16.2 Intro to Double Integrals A common application of double integrals is to use them for: 2 Calculus 1 Review: Area of a Region Between 2 Curves: The Iterated Integral Version of Area Between 2 Curves: 2 Vertically Simple Regions Versus Horizontally Simple Regions: Region is bounded by 1 a≤ x ≤ b and 8, (x) Sv≤8,(x) R a AT Area = LLdy (dx 8,(1) Vertically simple region page 2 Careful! Order of integration is important! dydx is: simple _simple dxdy is: x Region is bounded by c≤ y ≤ d and h₁(y) ≤x≤h₂(y) AREA OF A REGION IN THE PLANE 1.) If a region R is defined by: 2 R = = {(x, y): a≤x≤ b, g₁(x) ≤ y ≤ g₁(x)} where g₁ and g₂ are continuous on [a, b], then the area of the R is: d R 1) Ay A = 2.) If a region R is defined by: 2 (vertically simple) R = {(x, y): c≤ y ≤ d, h₁(y)≤x≤h₂(y)} where ½ and ½ are continuous on [c, d], then the area of the R is: h₁ Area = d h₂(y) h₁(1) IF dx (dy) Horizontally simple region 11, Χ 153 A (horizontally simple)
C3-16-16.1, 16.2 Intro to Double Integrals A common application of double integrals is to use them for: 2 Calculus 1 Review: Area of a Region Between 2 Curves: The Iterated Integral Version of Area Between 2 Curves: 2 Vertically Simple Regions Versus Horizontally Simple Regions: Region is bounded by 1 a≤ x ≤ b and 8, (x) Sv≤8,(x) R a AT Area = LLdy (dx 8,(1) Vertically simple region page 2 Careful! Order of integration is important! dydx is: simple _simple dxdy is: x Region is bounded by c≤ y ≤ d and h₁(y) ≤x≤h₂(y) AREA OF A REGION IN THE PLANE 1.) If a region R is defined by: 2 R = = {(x, y): a≤x≤ b, g₁(x) ≤ y ≤ g₁(x)} where g₁ and g₂ are continuous on [a, b], then the area of the R is: d R 1) Ay A = 2.) If a region R is defined by: 2 (vertically simple) R = {(x, y): c≤ y ≤ d, h₁(y)≤x≤h₂(y)} where ½ and ½ are continuous on [c, d], then the area of the R is: h₁ Area = d h₂(y) h₁(1) IF dx (dy) Horizontally simple region 11, Χ 153 A (horizontally simple)
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![C3-16-16.1, 16.2 Intro to Double Integrals
A common application of double integrals is to use them for:
2
Calculus 1 Review:
Area of a Region Between 2 Curves:
The Iterated Integral Version of Area Between 2 Curves:
2
Vertically Simple Regions Versus Horizontally Simple Regions:
Region is bounded by
1
a≤ x ≤ b and
8, (x) Sv≤8,(x)
R
a
AT
Area =
LLdy (dx
8,(1)
Vertically simple region
page 2
Careful! Order of integration is important!
dydx is:
simple
_simple
dxdy is:
x
Region is bounded by
c≤ y ≤ d and
h₁(y) ≤x≤h₂(y)
AREA OF A REGION IN THE PLANE
1.) If a region R is defined by:
2
R = = {(x, y): a≤x≤ b, g₁(x) ≤ y ≤ g₁(x)} where g₁ and g₂ are
continuous on [a, b], then the area of the R is:
d
R
1) Ay
A
=
2.) If a region R is defined by:
2
(vertically simple)
R = {(x, y): c≤ y ≤ d, h₁(y)≤x≤h₂(y)} where ½ and ½ are
continuous on [c, d], then the area of the R is:
h₁
Area =
d h₂(y)
h₁(1)
IF
dx (dy)
Horizontally simple region
11,
Χ
153
A
(horizontally simple)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F717b76b4-160b-4d09-bf30-5738b03be980%2F2b1f9023-90a0-483c-ae31-2bb33a5756a6%2Frm2uye8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:C3-16-16.1, 16.2 Intro to Double Integrals
A common application of double integrals is to use them for:
2
Calculus 1 Review:
Area of a Region Between 2 Curves:
The Iterated Integral Version of Area Between 2 Curves:
2
Vertically Simple Regions Versus Horizontally Simple Regions:
Region is bounded by
1
a≤ x ≤ b and
8, (x) Sv≤8,(x)
R
a
AT
Area =
LLdy (dx
8,(1)
Vertically simple region
page 2
Careful! Order of integration is important!
dydx is:
simple
_simple
dxdy is:
x
Region is bounded by
c≤ y ≤ d and
h₁(y) ≤x≤h₂(y)
AREA OF A REGION IN THE PLANE
1.) If a region R is defined by:
2
R = = {(x, y): a≤x≤ b, g₁(x) ≤ y ≤ g₁(x)} where g₁ and g₂ are
continuous on [a, b], then the area of the R is:
d
R
1) Ay
A
=
2.) If a region R is defined by:
2
(vertically simple)
R = {(x, y): c≤ y ≤ d, h₁(y)≤x≤h₂(y)} where ½ and ½ are
continuous on [c, d], then the area of the R is:
h₁
Area =
d h₂(y)
h₁(1)
IF
dx (dy)
Horizontally simple region
11,
Χ
153
A
(horizontally simple)
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