03 integral tak tentu
TRANSCRIPT
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TEKNIK PENGINTEGRALAN
• Metode substitusi
pengintegralan dengan substitusi dilakukan untuk menyederhanakan fungsi dengan variabel dalam fungsi sehingga fungsi dapat diintegralkan dengan mudah.
Pengintegralan dengan substitusi aljabar menggunakan persamaan:
dimana dan
duufdxxgxgf '
xgu dxxgdu '
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dxx
x
)(cos :1contoh
22
cx
cu
duu
duu
duu
duu
dxx
x
2
2
2
2
222
tan2
1
tan2
1
sec2
1cos
1
2
1cos
1
2
1
2
1
cos
1
)(cos
dxxdu
dxxdu
xu
2
1
2
:misal2
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dxx295
3 :2contoh
dxdu
xu
3
3
:misalu-a
du :integralbentuk
22
cx
arc
cu
arc
duu
dxx
5
3sin
5sin
5
1
95
322
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dxx
e x
2
16 :3contoh
dxx
du
dxx
du
xu
2
2
1
1
1
:misal
ce
ce
due
duedxx
e
x
u
u
ux
1
2
1
6
6
6
66
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dxe
ex
x
294 :4contoh
ce
arc
cu
arc
duu
duu
dxe
e
x
x
x
2
3tan
6
1
2tan
2
1
3
14
1
3
13
1
4
1
94
2
22
dxedu
dxedu
eu
x
x
x
3
1
3
3
:misalua
du :integralbentuk
22
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dxxx 11 :5contoh 43
cx
cu
duu
duu
duudxxx
234
23
21
43
116
13
2
4
14
14
14
111
dxxdu
dxxdu
xu
3
3
4
4
1
4
11
:misal
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Latihan Soal:
1.
2.
3.
4.
5.
dxxxx 343 330
4
dxxx cossin10
dxxxx 1266 25
3
dxxx10
2 4
dxxx 2
22
32