Kalkulus teknik integrasi 2
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Transcript of Kalkulus teknik integrasi 2
![Page 1: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/1.jpg)
McGraw-Hill/Irwin Copyright © 2008, The McGraw-Hill Companies, Inc. All rights reserved.
![Page 2: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/2.jpg)
Integral Substitusi Trigonometri
![Page 3: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/3.jpg)
Substitusi Trigonometri
1. Untuk
Misalkan
dengan
![Page 4: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/4.jpg)
Substitusi Trigonometri
2. Untuk
Misalkan
dengan
![Page 5: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/5.jpg)
Substitusi Trigonometri
3. Untuk
Misalkan
dengan dan
![Page 6: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/6.jpg)
Contoh :
Tentukan
Penyelesaian
![Page 7: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/7.jpg)
![Page 8: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/8.jpg)
![Page 9: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/9.jpg)
Contoh :
Tentukan
Penyelesaian
Misalkan
![Page 10: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/10.jpg)
![Page 11: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/11.jpg)
Contoh :
Tentukan
Penyelesaian
![Page 12: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/12.jpg)
Misalkan dan
![Page 13: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/13.jpg)
Contoh :
Tentukan
Penyelesaian
Integral Fungsi Rasional
![Page 14: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/14.jpg)
![Page 15: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/15.jpg)
![Page 16: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/16.jpg)
![Page 17: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/17.jpg)
Integral Fungsi Rasional
Contoh :
1. 1
1
x duu
1
Cx 1ln
2.
dxxx
x
84
122
dx
xx
x
84
5422
dxxx
dxxx
x
84
5
84
4222
![Page 18: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/18.jpg)
du
udx
xx
x 1
84
422
Cxx 84ln 2
dx
xxdx
xx 84
15
84
522
dx
x 4)2(
15
2
Cx
2
2tan
2
15 1
![Page 19: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/19.jpg)
Cx
xxdxxx
x
2
2tan
2
584ln
84
12 122
3. Faktor Linier Berbeda
dxx
x
9
352
dx
xx
x
)3)(3(
35
)3()3(9
352
x
B
x
A
x
x
)3)(3(
)3()3(
xx
xBxA
)3)(3(
33
xx
BBxAAx
![Page 20: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/20.jpg)
)3)(3(
)33()(
9
352
xx
BAxBA
x
x
5 BA
333 BA 1
5
BA
BA
42 B
2B3A
dxx
Bdx
x
Adx
x
x
)3()3(9
352
dx
xdx
x )3(
2
)3(
3
Cxx 3ln23ln3
![Page 21: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/21.jpg)
4. Faktor Linier Berulang
dxx
x2)3(
1
dxx
Bdx
x
A2)3()3(
22 )3()3()3(
1
x
B
x
A
x
x
2)3(
)3(
x
BxA
2)3(
3
x
BAAx13
1
BA
A4B
![Page 22: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/22.jpg)
dxx
dxx
dxx
x22 )3(
4
)3(
1
)3(
1
dxxx 2)3(43ln
duux 243ln
Cu
x 1
43ln
Cx
x
)3(
43ln
![Page 23: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/23.jpg)
5. Faktor Linier Berbeda dan Berulang
dxxx
xx2
2
)1)(3(
1383
22
2
)1()1()3()1)(3(
1383
x
C
x
B
x
A
xx
xx
2
2
)1)(3(
)3()1)(3()1(
xx
xCxxBxA
2
22
)1)(3(
3322
xx
CCxBBxBxAAxAx
2
2
)1)(3(
)33()22()(
xx
CBAxCBAxBA
dx
x
Cdx
x
Bdx
x
A2)1()1()3(
![Page 24: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/24.jpg)
1333
822
3
CBA
CBA
BA
13
8
3
331
122
011
C
B
A
OBE
2
1
4
C
B
A
![Page 25: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/25.jpg)
dxx
Cdx
x
Bdx
x
Adx
xx
xx22
2
)1()1()3()1)(3(
1383
dx
xdx
xdx
x 2)1(
2
)1(
1
)3(
4
dx
xdx
xdx
x 2)1(
12
)1(
1
)3(
14
Cx
xx
)1(
21ln3ln4
![Page 26: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/26.jpg)
6. Faktor Kuadrat Berbeda
dxxx
xx
)9)(12(
36322
2
912 2
x
CBx
x
A
912)9)(12(
363222
2
x
CBx
x
A
xx
xx
912
1292
2
xx
xCBxxA
912
2292
22
xx
CCxBxBxAAx
912
)9()2()2(2
2
xx
CAxCBxBA
![Page 27: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/27.jpg)
369
32
22
CA
CB
BA
36
3
2
109
210
021
C
B
A
0
3
4
C
B
AOBE
![Page 28: Kalkulus teknik integrasi 2](https://reader036.fdocument.pub/reader036/viewer/2022081421/559206241a28ab4c328b478a/html5/thumbnails/28.jpg)
dx
x
CBxdx
x
Adx
xx
xx
912)9)(12(
363222
2
dxx
xdx
x 9
3
12
42
dx
x
xdx
x 93
12
14
2
Cxx 9ln2
312ln2 2