Home - Filozofski fakultet Univerziteta u Zenici
Transcript of Home - Filozofski fakultet Univerziteta u Zenici
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Krivolinijski integrali druge vrste
1. Izračunaj krivolinijski integral od tačke A(1,0) do tačke B(0,2). ydyxdxxyIL 2)1(
a) po pravoj 2x+y=2 b) duž parabole 44 2 yxc) duž elipse x=cost ; y= 2sint Rješenja: a) Skicirajmo datu pravu (uputa vidi sliku desno). 2x+y=2 y = 2 - 2x dy = -2dx
111212
23
64
4)1264(
)44()122(
)2)(22(1)22(
)1(
0
1
0
1
20
1
30
1
42
0
1
3
320
1
2
20
1
2
1
xxxx
dxxxx
dxxxdxxx
dxxxdxxx
ydyxdxxyIL
b) Skicirajmo parabolu (uputa: vidi sliku iznad).
dyy
dxy
xyx24
1442
2
dyyy
ydyyyy
ydyyy
dyyy
y
ydyy
dyy
yy
ydyxdxxyIL
162282
1621
21
4
41
21
41)1(
532
0
42
422
0
3
222
0
22
2
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.15
17
15
45203012103
3
42
5
4
3
2
4
12
6
8
8
16
40
32
96
64
4
3
6840962
3
228162
0
22
0
32
0
42
0
52
0
62
0
2345
yyyyydy
yyyyy
c) Skicirajmo elipsu (uputa: vidi sliku sa prethodne stranice).
x = cost y = 2sint
dy = 2costdt
20
sin
cos
:3
t
ty
tx
L
3
4
3
22
3
121
4
14
3
sin2cos
4
cos4
3
sin
3cos
sincossin
4
cos
4sin
sin
cos
sincos
cossin2sinsincos4
)cossin2sinsincos4(sincos4)sincossin2(
cos2sin2cos)sin()1sin2(cos)1(
2
0
32
0
2
0
4
332
4433
2
0
2
0
22
0
3
22
0
332
0
2
2
0
22
3
tt
t
ct
cu
duudutdt
uttdtt
ct
cu
duu
dutdt
dutdt
ut
tdtt
tdtttdttdtt
dtttttttdttdtttt
tdttttdtttydyxdxxyIL
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