ITK-121 KALKULUS I
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Transcript of ITK-121 KALKULUS I
![Page 1: ITK-121 KALKULUS I](https://reader036.fdocument.pub/reader036/viewer/2022071808/56813215550346895d987083/html5/thumbnails/1.jpg)
ITK-121KALKULUS I
3 SKS
Dicky Dermawanwww.dickydermawan.890m.com
![Page 2: ITK-121 KALKULUS I](https://reader036.fdocument.pub/reader036/viewer/2022071808/56813215550346895d987083/html5/thumbnails/2.jpg)
INDEFINITE INTEGRAL – ANTIDERIVATIF
![Page 3: ITK-121 KALKULUS I](https://reader036.fdocument.pub/reader036/viewer/2022071808/56813215550346895d987083/html5/thumbnails/3.jpg)
F adalah anti turunan f
Jika
Contoh:
Notasi (seperti fungsi invers)
xfxF '
3xF
23 3xxD 323 xxA
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Fungsi Trigonometri
xxdx
dcossin Cxdxx sincos→
xxdx
dsincos Cxdxx cossin→
xxdx
d 2sectan Cxdxx tansec2→
xxdx
d 2csccot Cxx cotcsc2→
xxxdx
dtansecsec Cxdxxx sectansec→
xxxdx
dcotcsccsc Cxxx csccotcsc→
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Invers Fungsi Trigonometri
2
1
1
1sin
xx
dx
d
Cxx
dx 1
2sin
1→
2
1
1
1cos
xx
dx
d
Cxx
dx 1
2cos
1→
Cxx 11 cossin
21
1
1tan
xx
dx
d
Cx
x
dx 12
tan1→
21
1
1cot
xx
dx
d
Cx
x
dx
12
cot1
→
Cxx 11 cottan
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1
1sec
2
1
xxx
dx
d
Cx
xx
dx 1
2sec
1
1
1csc
2
1
xxx
dx
dCx
xx
dx
1
2csc
1
→
Cxcscxsec 11
→
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Fungi Transenden
xx eedx
d Cedxe xx
→
eln
alna
elog
aa
dx
d x
a
xx Cadxalna xx →
xx
dx
d 1ln Cxln
x
dx→
eax
e
x
ex
dx
d aa
ln
lnloglog Cxlogdx
x
elog aa
→
![Page 8: ITK-121 KALKULUS I](https://reader036.fdocument.pub/reader036/viewer/2022071808/56813215550346895d987083/html5/thumbnails/8.jpg)
Sifat-Sifat
dxxfkdxxfk
dxxgdxxfdxxgxf
dxxgdxxfdxxgxf
![Page 9: ITK-121 KALKULUS I](https://reader036.fdocument.pub/reader036/viewer/2022071808/56813215550346895d987083/html5/thumbnails/9.jpg)
Contoh
dxx4x3 2
1x
dx2
1x
dxx2
![Page 10: ITK-121 KALKULUS I](https://reader036.fdocument.pub/reader036/viewer/2022071808/56813215550346895d987083/html5/thumbnails/10.jpg)
SOAL
1
2
3
4
dxx35
dxx 31
dxx118
dxx3 2
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SOAL
5
6
7
8
2
6
x
dx
dxex2
5
3x
dx
21
5
x
dx
![Page 12: ITK-121 KALKULUS I](https://reader036.fdocument.pub/reader036/viewer/2022071808/56813215550346895d987083/html5/thumbnails/12.jpg)
9
10
11
12
1
62xx
dx
21
5
x
dx
dx
x
x3
3
1
4
dx
e
ex
x
1
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13
14
15
16
dxx
x
cos1
sin
x
dx
31
dxx
x2
21
dxx
x21
21
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17
18
19
20
dxx22 3
dxe x2
1
dxxx 231
dxx
x1
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21
22
23
24
dx
x
xx 13 22
dxxx cos2sin3
dxxx sin23 2
dx31x3 4
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25
26
27
28
dxxx32 42
dxxx732 18515
dxxxx 322322
dxxx354 92
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29
30
31
32
dxxx 733 2
dxxxx632 83515
dxxx 3 2 1123
dx
x
x
52
32
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33
34
35
36
dxxx 2sin2cos4
dxxxx 225 cossin
dxxx 13sin13cos
dxxx cossin 4
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37
38
39
40
dxxx32 1
dxxx 232 1
dxxx 24 1
dxxx 34 1