1 / 8

Integral Fungsi Rasional Pecah Rasional

Integral Fungsi Rasional Pecah Rasional Bentuk umum Integral Fungsi Rasional Pecah Rasional : , I ntegral fungsi rasional pecah dibagi menjadi 4 bentuk sebagai berikut : I. Jika g(x) merupakan faktor fungsi linier tidak berulang :

tekli
Download Presentation

Integral Fungsi Rasional Pecah Rasional

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Integral FungsiRasionalPecah Rasional Bentukumum Integral FungsiRasionalPecah Rasional:, Integralfungsirasionalpecahdibagimenjadi 4 bentuksebagaiberikut : I. Jikag(x) merupakanfaktorfungsi linier tidakberulang: II Jika g(x) merupakanfaktorfungsi linier ada yang berulang: III, Jika g(x) merupakanfaktorfungsi linier danfungsikwadrat: Jika g(x) merupakanfaktorfungsikwadrat yang berbeda” Denganmetodekoefisientaktentudicarikonstanta A,B,C, D dan E

  2. RumusDasar Integral yang digunakan: Contoh: Jawab: = Kesamaan:

  3. . Maka 9x-1 = A(2x-1) + B(x+3) Untuk x=1/2 maka (9/2)-1 = 0 + B ( ½+3) 3 ½ = 3 ½ B  B = 1 Untuk x= -3 maka 27-1 = A(-3-3) 26= -6AA= -26/6

  4. . Jawab: Kesamaan” Maka x = A(x-2)(x+4) + B ( x+4) + C ( x-2)2 Untuk x =2  2= 0 + B ( 2+4) 2 = 6 B B = 1/3 Untuk x = -4  -4 = 0 + 0 + C ( -4-2)2 -4 = 36 C C =-1/9

  5. Untukx = 0  0 = A (-2)(4) +B4 + C (-2)2 0 = -8 A + 4/3- 4/9 -8/9 = -8 A A = - 1/9 = - 1/9 ln | x-2| - 1/3( x-2 )-1 – 1/9 ln|x+4| + C Jawab Kesamaan”

  6. Maka 2x + 6 = A ( x2 +1) + (Bx+C)(4x-1) Koefisien x2  0 = A + 4B  A= - 4B --,,-- x  2 = -B + 4 C KoefisienKonstan 6 = A -C  6= -4B –C 24 = - 16 B – 4 C 2 = - B + 4 C _________________ + 26 = - 17 B B = - 26/17  A = 104/17 4C = 2 + B4C = 2 – 26/17 4C = 8/17 C = 2/17

  7. . Jawab: Kesamaan: Maka : 2x+6 = (Ax+B)(x2+1) + (Cx+D)(x2+3) Menyamakan koefisien dari x ruas kiri dan ruas kanan: Koefisien : x3 : 0 = A + C  A = - C " - x2 : 0 = B +D  B= - D - " - x : 2 = A + 3 C2=-C+3C  2 C = 2 maka C = 1 dan A = -1 - " - konstan : 6 = B + 3 D  6 = -D + 3 D  D = 3 dan B = - 3

  8. TUGAS :  Hitung integral fungsidibawahini :

More Related