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Bab IV INTEGRAL

Bab IV INTEGRAL. IR. Tony hartono bagio , mt , mm. IV. INTEGRAL. 4.1 Rumus Dasar 4.2 Integral dengan Subsitusi 4.3 Integral Parsial 4.4 Integral Hasil = ArcTan dan Logaritma 4.5 Integral Fungsi Pecah Rasional 4.6 Integral Fungsi Trigonometri 4.7 Integral Fungsi Irrasional.

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Bab IV INTEGRAL

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  1. Bab IVINTEGRAL IR. Tony hartonobagio, mt, mm Prepared by : Tony Hartono Bagio

  2. IV. INTEGRAL 4.1 RumusDasar 4.2 Integral denganSubsitusi 4.3 Integral Parsial 4.4 Integral Hasil = ArcTandanLogaritma 4.5 Integral FungsiPecahRasional 4.6 Integral FungsiTrigonometri 4.7 Integral FungsiIrrasional Prepared by : Tony Hartono Bagio

  3. 4.6 Integral FungsiTrigonometri Prepared by : Tony Hartono Bagio 4.6.1 Rumus-rumusSederhana ∫cosx dx = sin x + C ∫tan x dx = – ln|cos x|+ C ∫sin x dx = – cos x + C ∫cot x dx = ln |sin x|+ C ∫sec2x dx = tan x + C ∫sec x tan x dx = sec x + C ∫csc2x dx = – cot x + C ∫csc x cot x dx = – csc x + C ∫sec x dx = ln |sec x + tan x| + C ∫csc x dx = – ln |csc x + cot x| + C

  4. 4.6 Integral FungsiTrigonometri Prepared by : Tony Hartono Bagio 4.6.2 Bentuk ∫ R(sin x) cos x dx dan ∫ R(cos x) sin x dx Jika R fungsi rasional maka ∫ R(sin x) cos x dx = ∫ R(sin x) d(sin x) = ∫ R(y) dy ∫ R(cos x) sin x dx = – ∫ R(cos x) d(cos x) = –∫ R(t) dt Ingat rumus cos2 x + sin2 x = 1, maka: ∫ R(sin x, cos2 x) cos x dx = ∫ R( y, 1− y2 ) dy ∫ R(cos x, sin2 x) sin x dx = – ∫ R(t, 1− t2 ) dt Contoh 1. ∫(2cos2x − sin x + 7) cos x dx 2. ∫sin3x dx

  5. 4.6 Integral FungsiTrigonometri Prepared by : Tony Hartono Bagio

  6. 4.6 Integral FungsiTrigonometri Prepared by : Tony Hartono Bagio

  7. 4.6 Integral FungsiTrigonometri Prepared by : Tony Hartono Bagio 4.6.3 Integral denganmemperhatikan

  8. 4.6 Integral FungsiTrigonometri Prepared by : Tony Hartono Bagio

  9. 4.6 Integral FungsiTrigonometri Prepared by : Tony Hartono Bagio

  10. 4.6 Integral FungsiTrigonometri Prepared by : Tony Hartono Bagio

  11. 4.6 Integral FungsiTrigonometri Prepared by : Tony Hartono Bagio

  12. 4.6 Integral FungsiTrigonometri Prepared by : Tony Hartono Bagio

  13. 4.6 Integral FungsiTrigonometri Prepared by : Tony Hartono Bagio

  14. 4.6 Integral FungsiTrigonometri Prepared by : Tony Hartono Bagio 4.6.4 Substitusi JikaR(sin x, cosx) fungsirasionaldalam sin x dancosx, maka∫ R(sin x, cosx) dxdapatdibawamenjadiintegral fungsirasionaldalamy denganmenggunakansubstitusi

  15. 4.6 Integral FungsiTrigonometri Prepared by : Tony Hartono Bagio

  16. 4.6 Integral FungsiTrigonometri Prepared by : Tony Hartono Bagio

  17. 4.6 Integral FungsiTrigonometri Prepared by : Tony Hartono Bagio

  18. 4.6 Integral FungsiTrigonometri Prepared by : Tony Hartono Bagio

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