ITK-121KALKULUS I

3 SKS

Dicky Dermawanwww.dickydermawan.890m.com

INDEFINITE INTEGRAL – ANTIDERIVATIF

F adalah anti turunan f

Jika

Contoh:

Notasi (seperti fungsi invers)

xfxF '

3xF

23 3xxD 323 xxA

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→

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

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

→

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

→

Sifat-Sifat

dxxfkdxxfk

dxxgdxxfdxxgxf

dxxgdxxfdxxgxf

Contoh

dxx4x3 2

1x

dx2

1x

dxx2

SOAL

1

2

3

4

dxx35

dxx 31

dxx118

dxx3 2

SOAL

5

6

7

8

2

6

x

dx

dxex2

5

3x

dx

21

5

x

dx

9

10

11

12

1

62xx

dx

21

5

x

dx

dx

x

x3

3

1

4

dx

e

ex

x

1

13

14

15

16

dxx

x

cos1

sin

x

dx

31

dxx

x2

21

dxx

x21

21

17

18

19

20

dxx22 3

dxe x2

1

dxxx 231

dxx

x1

21

22

23

24

dx

x

xx 13 22

dxxx cos2sin3

dxxx sin23 2

dx31x3 4

25

26

27

28

dxxx32 42

dxxx732 18515

dxxxx 322322

dxxx354 92

29

30

31

32

dxxx 733 2

dxxxx632 83515

dxxx 3 2 1123

dx

x

x

52

32

33

34

35

36

dxxx 2sin2cos4

dxxxx 225 cossin

dxxx 13sin13cos

dxxx cossin 4

37

38

39

40

dxxx32 1

dxxx 232 1

dxxx 24 1

dxxx 34 1