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KELOMPOK 1B
1. Julio Yordan D021191029
2. Effendy Kho D021201004
3. Muh. Akbar Buata D021201012
4. Muh. Ahsan Ridwan D021201029
5. Mutiara Farisah Ramdhani D021201044
6. Fathur Rahman Sigara D021201064
7. Ardiansyah D021201106
KELOMPOK 1B
KELOMPOK 1B
METODE
INTEGRAL
SIMPSON
KELOMPOK 1B
DEFINISI
Metode integrasi Simpson merupakan
pengembangan metode integrasi trapezoida,
hanya saja daerah pembaginya bukan
berupa trapesium tetapi berupa dua buah
trapesium dengan menggunakan pembobot
berat di titik tengahnya seperti telihat pada
gambar berikut ini. Atau dengan kata lain
metode ini adalah metode rata-rata dengan
pembobot kuadrat
KELOMPOK 1B
Bila menggunakan trapesium luas bangun di atas:
Pemakaian aturan Simpson di mana bobot f1 sebagai titik tengah dikalikan dengan 2 untuk
menghitung luas bangun di atas dapat dituliskan dengan:
KELOMPOK 1B
Perhatikan gambar berikut:
Dengan menggunakan aturan Simpson, luas dari daerah
yang dibatasi fungsi y = f(x) dan sumbu X dapat dihitung
sebagai berikut:
Atau dapat ditulis dengan:
Dibandingkan dengan hasil perhitungan kalkulus, maka kesalahannya sangat kecil
KELOMPOK 1B
Logaritma Integral Simpson
1. Definisikan y = f(x)
2. Tentukan batas bawah (a) dan batas atas integrasi (b)
3. Tentukan jumlah pembagi (n)
4. Hitung h = (b-a) / n
5. Hitung
KELOMPOK 1B
Contoh Soal
KELOMPOK 1B
TERIMA KASIH

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INTEGRAL SIMPSON.pptx

  • 1. KELOMPOK 1B 1. Julio Yordan D021191029 2. Effendy Kho D021201004 3. Muh. Akbar Buata D021201012 4. Muh. Ahsan Ridwan D021201029 5. Mutiara Farisah Ramdhani D021201044 6. Fathur Rahman Sigara D021201064 7. Ardiansyah D021201106 KELOMPOK 1B
  • 3. KELOMPOK 1B DEFINISI Metode integrasi Simpson merupakan pengembangan metode integrasi trapezoida, hanya saja daerah pembaginya bukan berupa trapesium tetapi berupa dua buah trapesium dengan menggunakan pembobot berat di titik tengahnya seperti telihat pada gambar berikut ini. Atau dengan kata lain metode ini adalah metode rata-rata dengan pembobot kuadrat
  • 4. KELOMPOK 1B Bila menggunakan trapesium luas bangun di atas: Pemakaian aturan Simpson di mana bobot f1 sebagai titik tengah dikalikan dengan 2 untuk menghitung luas bangun di atas dapat dituliskan dengan:
  • 5. KELOMPOK 1B Perhatikan gambar berikut: Dengan menggunakan aturan Simpson, luas dari daerah yang dibatasi fungsi y = f(x) dan sumbu X dapat dihitung sebagai berikut: Atau dapat ditulis dengan: Dibandingkan dengan hasil perhitungan kalkulus, maka kesalahannya sangat kecil
  • 6. KELOMPOK 1B Logaritma Integral Simpson 1. Definisikan y = f(x) 2. Tentukan batas bawah (a) dan batas atas integrasi (b) 3. Tentukan jumlah pembagi (n) 4. Hitung h = (b-a) / n 5. Hitung