5 beli̇rli̇ i̇ntegral
TRANSCRIPT
BELİRLİ İNTEGRAL KURALLARI
VE SORULARIN ÇÖZÜMLERİ
BELİRLİ İNTEGRAL
KURALLAR
02
)(
4
4
24
4
xxdx
dxxfAa
b
1)
2
3
2
1
2
2
2
22
2
1
22
1
2
1
x
x
xxdx
)()(
)()()()(
)()()(
aFcF
bFcFaFbF
dxxfdxxfdxxfc
b
b
a
c
a
Ör 1):
2)
12
12
2
20
2
11
22
111
22
2
1
21
0
2
2
1
1
0
2
0
xxx
xI
dxxdxxdxx
12
1
2
1
Ör:
xdxxdx
x
x
x
x
dxx
sgnsgn
0,1
0,0
0,1
sgn
)(sgn
1
0
0
1
1
1
Ör:
2
01)1(0
1
1
0
0
1
1
0
0
1
xx
dxdx
3)
çiftxxxfxf
tekxxxfxf
çif txfdxxf
tekxf
dxxf
dxxfdxxf
a
a
a
a
b
b
a
cos)cos(),()(
sin)sin(),()(
)(,)(2
)(,0
)(
)()(
0
dxxf
dxxf
dxxfdxxfdxxf
a
a
a
a
a
a
)(
)(
)()()(
0
0
0
04)
xdxdu
ux
xdx
sin
cos
sincos
11
2
32
0
5
2
5
2
2
5
02
cos,2
1
10cos,0
0
1
2
5
2
30
1
21
11
uduuI
ux
ux
Ör:
512)1(1
2
2
3
3
23)(
31,2
12,3)(
2233
2
1
21
1
3
2
1
21
1
3
2
1
21
1
2
1
2
xxxx
xdxdxxdxxf
isexx
isexxxfÖr:
2
121
010
101
?2
1
x
xx
xx
xx
dxxx
xdxdxxdxx2
1
1
0
0
1
)0()1(
Ör:
22
12
2
1
2
1
2
2
2
)1(0
22
2222
1
22 xx
21
20
21
)24sgn(
)24sgn(33
1
x
x
x
x
dxxxÖr:
2
25
4
50
4
16
4
81
4
1
4
16
4
2
4
3
4
1
4
2
44
)1(1
4444
3
2
42
1
4
33
1
32
1
xx
dxxdxxI
2ln
12ln13ln1ln)1(
1
ln
)1()1(
1
3
2
xx
ctt
dt
dtdxtxdxx
1. YOL
2ln1ln2lnln
213,112
321
)1(
2
1
2
1
21
21
3
2
tt
dt
tt
xxtx
t
dt
x
dx
2. YOL
5
32
5
0
5
32
5
2222
0000
)12(
)12()(
2
0
54
2
0
2
22
2
11
2
422
0
tdttI
tx
tx
dtdxxtxxI
dxxxxÖr:
eeedte
t
t
dtdxxtxx
dxex
tu
xx
33
1
3
1
2
2
2
1
2
11
0
3111
1100
)12()1(
)12(2
Ör: