pt 3 integral tak tentu-d4
TRANSCRIPT
![Page 1: Pt 3 integral tak tentu-d4](https://reader038.vdocuments.net/reader038/viewer/2022102407/587a43df1a28ab00148b4ea9/html5/thumbnails/1.jpg)
MATEMATIKA
Oleh:Dr. Parulian Silalahi, M.Pd
![Page 2: Pt 3 integral tak tentu-d4](https://reader038.vdocuments.net/reader038/viewer/2022102407/587a43df1a28ab00148b4ea9/html5/thumbnails/2.jpg)
Defenisi:
Misalkan F(x) adalah suatu fungsi umum yang bersifat F’(x) = f(x) atau F(x) dapat dideferensialkan sehingga F’(x) = f(x). Dalam hal demikian, maka F(x) dinamakan sebagai himpunan anti-pendiferensialan (anti-turunan) atau himpunan pengintegralan dari fungsi F’(x) = f(x)
![Page 3: Pt 3 integral tak tentu-d4](https://reader038.vdocuments.net/reader038/viewer/2022102407/587a43df1a28ab00148b4ea9/html5/thumbnails/3.jpg)
Notasi IntegralPengintegralan fungsi f(x) terhadap x yang ditulis dalam
bentuk dinamakan sebagai integral tak tentu dari fungsi f(x) terhadap x
= F(x) + C
F(x) dinamakan fungsi integral umum dan F(x) bersifat F’(x) = f(x)
• f(x) disebut fungsi integran
• C konstanta real sembarang dan sering disebut sebagai konstanta pengintegralan.
dxxf )(
dxxf )(
![Page 4: Pt 3 integral tak tentu-d4](https://reader038.vdocuments.net/reader038/viewer/2022102407/587a43df1a28ab00148b4ea9/html5/thumbnails/4.jpg)
Rumus Dasar Fungsi Aljabar
cxxdx
ndanrasionalbilanganndenganCxnadxax
ndanrasionalbilanganndenganCxn
dxx
dxxgdxxfdxxgxf
caxadx
cxdx
nn
nn
ln.6
1,1
.5
1,11.4
)()()()(.3
.2
.1
1
1
![Page 5: Pt 3 integral tak tentu-d4](https://reader038.vdocuments.net/reader038/viewer/2022102407/587a43df1a28ab00148b4ea9/html5/thumbnails/5.jpg)
CONTOH 1:
Tentukanlah integral dari fungsi berikut ini:
dxx
xx
dxxx
dxx
dxx
)35(.4
)74(.3
3.2
.1
35 34
22
8
7
![Page 6: Pt 3 integral tak tentu-d4](https://reader038.vdocuments.net/reader038/viewer/2022102407/587a43df1a28ab00148b4ea9/html5/thumbnails/6.jpg)
Jawab:
Cxx
dxxdxxdxxx
CxCxdxx
CxCxdxx
13
2222
9188
8177
734
74)74(.3
93
1833.2
81
171.1
![Page 7: Pt 3 integral tak tentu-d4](https://reader038.vdocuments.net/reader038/viewer/2022102407/587a43df1a28ab00148b4ea9/html5/thumbnails/7.jpg)
Cxxx
Cxxx
dxxdxxdxx
dxx
dxxdxxdxx
xx
258
5
131
53
14
353
4
35 34
35 34
23
85
133
11
145
35
35)35(.4
53
![Page 8: Pt 3 integral tak tentu-d4](https://reader038.vdocuments.net/reader038/viewer/2022102407/587a43df1a28ab00148b4ea9/html5/thumbnails/8.jpg)
Rumus Dasar Integral Tak Tentu Fungsi Trigonometri
Cecxecxdxx
Cxxdxx
Cxxdxec
Ctgxxdx
Cxxdx
Cxxdx
coscos.cot.6
secsec.tan.5
cotcos.4
sec.3
sincos.2
cossin.1
2
2
![Page 9: Pt 3 integral tak tentu-d4](https://reader038.vdocuments.net/reader038/viewer/2022102407/587a43df1a28ab00148b4ea9/html5/thumbnails/9.jpg)
Integral Tak Tentu Fungsi TrigonometriDengan Variabel Sudut (ax +b)
Cbaxecdxbaxecbax
Cbaxdxbaxbax
Cbaxdxbaxec
Cbaxtgdxbax
Cbaxdxbax
Cbaxdxbax
a
a
a
a
a
a
)(cos)(cos).cot(.6
)sec()sec().tan(.5
)cot()(cos.4
)()(sec.3
)sin()cos(.2
)cos()sin(.1
1
1
12
12
1
1
![Page 10: Pt 3 integral tak tentu-d4](https://reader038.vdocuments.net/reader038/viewer/2022102407/587a43df1a28ab00148b4ea9/html5/thumbnails/10.jpg)
dxxxtg
dxxxec
dxxx
)75(sec).75(.3
)6(sec)2(cos.2
)5cos()43sin(.122
![Page 11: Pt 3 integral tak tentu-d4](https://reader038.vdocuments.net/reader038/viewer/2022102407/587a43df1a28ab00148b4ea9/html5/thumbnails/11.jpg)
Jawab:
Cxx
dxxx
)5sin()43cos(
)5cos()43sin(.1
51
31
Cxx
dxxxec
)6tan()2cot(
)6(sec)2(cos.2
61
21
22
![Page 12: Pt 3 integral tak tentu-d4](https://reader038.vdocuments.net/reader038/viewer/2022102407/587a43df1a28ab00148b4ea9/html5/thumbnails/12.jpg)
Jawab:
Cx
dxxxtg
)75sec(
)75(sec).75(.3
51
![Page 13: Pt 3 integral tak tentu-d4](https://reader038.vdocuments.net/reader038/viewer/2022102407/587a43df1a28ab00148b4ea9/html5/thumbnails/13.jpg)
Menentukan Integral dengan Cara Subsitusi
CONTOH 3:Tentukanlah integral dari fungsi berikut ini:
dxxx
xdxx
dxxx
dxx
)5cos(2.4
cossin.3
82.2
)74(.1
2
2
2
5
![Page 14: Pt 3 integral tak tentu-d4](https://reader038.vdocuments.net/reader038/viewer/2022102407/587a43df1a28ab00148b4ea9/html5/thumbnails/14.jpg)
Jawab:
dxx 5)74(.1
Misalkan u = (4x + 7), maka du = 4 dx atau dx = ¼ du
Sehingga dapat diubah menjadi
Cx
Cuduu
6
241
6151
415
41
)74(
.
dxx 5)74(
![Page 15: Pt 3 integral tak tentu-d4](https://reader038.vdocuments.net/reader038/viewer/2022102407/587a43df1a28ab00148b4ea9/html5/thumbnails/15.jpg)
Misalkan u = (2x2 + 8), maka du = 4x dx atau dx = 1/4x du
Sehingga dapat diubah menjadi dxxx 82 2
Cx
Cu
Cu
duuduux x
23
23
21
21
)82(
.
.
261
61
111
41
41
41
dxxx 82.2 2
![Page 16: Pt 3 integral tak tentu-d4](https://reader038.vdocuments.net/reader038/viewer/2022102407/587a43df1a28ab00148b4ea9/html5/thumbnails/16.jpg)
Misalkan u = sin x, maka du = cos x dx atau dx = 1/cosx du
Sehingga dapat diubah menjadi
xdxx cossin.3 2
xdxx cossin 2
Cx
Cu
duux
duxuxdxx
331
331
2
22
sin
cos.coscossin
![Page 17: Pt 3 integral tak tentu-d4](https://reader038.vdocuments.net/reader038/viewer/2022102407/587a43df1a28ab00148b4ea9/html5/thumbnails/17.jpg)
Misalkan u = x2 - 5, maka du = 2x dx atau dx = 1/2x du
Sehingga dapat diubah menjadi dxxx )5cos(2 2
Cx
Cu
duu
xduuxdxxx
)5sin(
sin
cos
2cos2)5cos(2
2
2
dxxx )5cos(2.4 2
![Page 18: Pt 3 integral tak tentu-d4](https://reader038.vdocuments.net/reader038/viewer/2022102407/587a43df1a28ab00148b4ea9/html5/thumbnails/18.jpg)
TERIMA KASIHSelamat Belajar