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Approximate Integration

Approximate Integration. Materi 7.4 Bab. Integral Riemann Buku Intro. To Real Analysis. Kelompok 4: Pratiwi Nusi (P3500211008) Samsu Alam (P3500211010). Approximate Integration. Tujuan :. Memahami konsep pendekatan ( aproksimasi ) dalam pengintegalan .

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Approximate Integration

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  1. Approximate Integration Materi 7.4 Bab. Integral Riemann Buku Intro. To Real Analysis Kelompok 4: PratiwiNusi (P3500211008) SamsuAlam (P3500211010)

  2. Approximate Integration Tujuan : • Memahamikonseppendekatan (aproksimasi) dalampengintegalan. • Memahamipendekatanpengintegralanberdasarkanpartisi yang sama. • Memahamibeberapateknikpendekatanpengintegralanmenggunakanaturan Trapezoid, aturan Midpoint danaturanSimpson.

  3. KonsepAproksimasi Prosedurdasardalammemperolehtaksiransecaracepatdarifungsiberdasarkanteorema 7.1.4(c) dapatdituliskanbahwajika maka Jikaintegral dari g dan h dapatdihitung, makadapatdiperolehbatasdari yang cukupakuratuntukkebutuhanpenaksiran Selainitujugadapatdilakukanpendekatanpengintegralandenganmenerapkanteorema Taylor padasuatu polynomial

  4. PendekatanPengintegralanberdasarkanpartisi yang sama dari kontinu, partisi dalam sub interval sama yang mempunyaipanjang Karenanyaadalahpartisi • Kemudiandenganmengambiltitikujungkiridankanan subinterval diperolehperkiraankiridankanan yang rata-ratanyadapatdinyatakansebagai:

  5. sehinggamenurutTeorema 7.4.1 Jika maka Monoton, dandiberikan

  6. MetodePendekatanPengintegralan A. Aturan Trapezoid B. Aturan Midpoint C. Aturan Simpson

  7. A. Aturan Trapezoid Misalkanfkontinupada[a, b]. Aturan Trapezoid untukmemperkirakanhasildari y x …

  8. B. Aturan Midpoint y Misalkanfkontinupada[a, b]. Aturan Midpoint untukmemperkirakanhasildari a … b

  9. C. Aturan Simpson Misalkanfkontinupada[a, b]. Aturan Simpson untukmemperkirakanhasildari y x …

  10. Contoh: (a) Trapezoidal Rule (b) Midpoint Rule (c) Simpson’s Rule

  11. Thank You Referensi:

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