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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 :

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Integral Fungsi Rasional Pecah Rasional

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  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 :

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