1 / 18

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.

aurorette-davon
Télécharger la présentation

Bab IV INTEGRAL

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. 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

More Related