integral garis 2
DESCRIPTION
Matematika TeknikTRANSCRIPT
Teorema Green’s
Contoh 2 :
D(0,0)
F(1,1)
E(1,0)
G(0,1)
R
y
x0
thoerem.sGreen' verify and integral doble tointegral line eConvert th b.
G90,1) and F(1,1) E(1,0), D(0,0), rtices with ve
square theof sides thearound Evaluate a. 2dyxydxxR
+∫
∫∫∫∫ ∫ +++=D
G
G
F
F
EC
E
D
[ ]21
211
2
0100
`1
210
0
1
1
0
2
=−=⎥⎦
⎤⎢⎣
⎡+=
+++=+ ∫∫ ∫xy
xdxdydyxxydxC
0to1fromdecreases and 00 GD,On 0to1fromdecreases and 01 FG,On
10 and 01 EF,On 10 and 00 DE,On
y, dxxx, dyy
y, dxxx, dyy
====
≤≤==≤≤==
D(0,0)
F(1,1)
E(1,0)
G(0,1)
R
y
x0
Teorema Green’s
21
21
21
2
)2(
and2
),(and),(
1
0
1
0
1
0
1
0
2
1
0
1
0
2
2
=⎥⎦⎤
⎢⎣⎡=
=⎥⎦
⎤⎢⎣
⎡=
=
−=+
=∂∂
=∂∂
==
∫∫
∫∫∫∫∫
y
dyx
xdxdy
dxdyxxdyxxydx
xyPx
xQ
xyxQxyyxP
RC
Integral garis
Contoh 2 :
Contoh 2 :
Integral Permukaan
Contoh 2 :
Contoh 2 :
Teorema Stoke’s
Contoh 2 :
Teorema Gauss
Contoh 2 :
