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. Integral Parsial Jika u dan v merupakan fungsi dapat diturunkan terhadap x maka

. Integral Parsial Jika u dan v merupakan fungsi dapat diturunkan terhadap x maka .d( uv ) = u dv +v du .u dv = d( uv ) – v du Integral dengan bentuk ini disebut integral parsial . Contoh :

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. Integral Parsial Jika u dan v merupakan fungsi dapat diturunkan terhadap x maka

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  1. . Integral Parsial Jika u dan v merupakanfungsidapatditurunkanterhadap x maka .d(uv) = u dv +v du .u dv = d(uv) – v du Integral denganbentukinidisebut integral parsial. Contoh: 1 `. u = ln x dan du = dx .du = 1/x dx , v = 1/2 x2 = ½ x2ln x – (1/2)(1/2 x2) = ½ x2ln x – ¼ x2 + C

  2. . u = x dandv = sin x dx Jawab: du = dx , v = - cos x = - x cosx + sin x + C u = x2dandv = exdx du = 2x dxdan v = ex = x2 ex - 2x ex + 2 = x2 ex - 2x ex + 2 ex + C//

  3. RumusReduksi di Integral : Integral DenganSubstitusiTrigoniometri Suatubentukintegran yang terdiridarisalahsatubentuk, atautetapibukanfaktorirasional lain makadapatdigunakansubstitusitrigoniometrisebagaiberikut :

  4. 1.Untukgunakan x= a sin u untukmemperoleh=a cosu 2.Untukgunakan x= a tg u untukmemperoleh=a sec u 3.Untukgunakan x= a sec u untukmemperoleh=a tg u Untuktiapbentukintegrasimenghasilkanpernyataandalamvariabel u. Contoh: jawab Misalx= 2 sin u maka= 2 cos u dx = 2 cos u du == 4= 4{1/2 cos u sin u + ½ u} = 2 cos u sin u + 2 arc sin x/2 + C = . (x/2) + 2 arc sin x/2 + C

  5. . = -½ { 2/3 U3/2 } + C =-1/3 (4-x2)3/2 +C

  6. = 1/3 sec2x tgx– 4/3 tgx +x +C/// = - 1/3cosec2ctg x -2/3ctg x + C TUGAS Hitung integral fungsidibawahini :

  7. .

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