3.9. Divergence theorem
another way to evaluate f) Eds BUI hows
-
should be d closed surface s
{ Flux int}
Divergence
-
theorem
- -
1-
orange → Q
- .
I bounded I
let Q be a solid
region
1
1
by a closed surfaces oriented
outward normal vector
by !
1
.if pee / →s
1 Then JS Sssdivridv
-
:
rids = '
' I
s Q
1- -
- - -
-
-
-
- -
-
examples
1. Determine JSÉDJ using suitable theorem
s outer sur -
fate of solid
region bounded by 2-
=
4- K
' -
y
'
and 1- =3 and F- =
<
y,
-
×
,
22-7
① ri split 5=51 V52
? paraboloid ' disk
-
y >
Y But now we see we have a
surface
=
divergence theorem
%
③ f) E. d- =D) 2dV
① f- = <
y -21,2
t >
S Q
volume
iii.
,
' →
of
divf 8. F- Rt > Q
Pray
=
= = <
,
;
-
, ,
§
,
Dot -1012
}
=
0 =
get intersection
product 1 '
:3
4- v2 -
y
"
"
%[
≤ o≤ 21T
④
◦ '
◦ ≤ r≤ ,
E)2) ◦
rdzdrdo → vinyl :|
cylindrical coordinates
'
3 ≤ 2- ≤ 4- r
(
↓ ↓ =ñ→ r, 0,7 )
plane paraboloid
another way to evaluate f) Eds BUI hows
-
should be d closed surface s
{ Flux int}
Divergence
-
theorem
- -
1-
orange → Q
- .
I bounded I
let Q be a solid
region
1
1
by a closed surfaces oriented
outward normal vector
by !
1
.if pee / →s
1 Then JS Sssdivridv
-
:
rids = '
' I
s Q
1- -
- - -
-
-
-
- -
-
examples
1. Determine JSÉDJ using suitable theorem
s outer sur -
fate of solid
region bounded by 2-
=
4- K
' -
y
'
and 1- =3 and F- =
<
y,
-
×
,
22-7
① ri split 5=51 V52
? paraboloid ' disk
-
y >
Y But now we see we have a
surface
=
divergence theorem
%
③ f) E. d- =D) 2dV
① f- = <
y -21,2
t >
S Q
volume
iii.
,
' →
of
divf 8. F- Rt > Q
Pray
=
= = <
,
;
-
, ,
§
,
Dot -1012
}
=
0 =
get intersection
product 1 '
:3
4- v2 -
y
"
"
%[
≤ o≤ 21T
④
◦ '
◦ ≤ r≤ ,
E)2) ◦
rdzdrdo → vinyl :|
cylindrical coordinates
'
3 ≤ 2- ≤ 4- r
(
↓ ↓ =ñ→ r, 0,7 )
plane paraboloid
