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KALKULUS 2
by:
Teti Desyani, M.Kom.
PERTEMUAN 1
PENGANTAR INTEGRAL
DESKRIPSI
• Integral merupakan anti turunan atau kebalikan dari turunan.
• Notasi integral :
• tokoh yang mengembangkan dan memperkenalkan konsep differensial dan anti-
differensial (integral) dalam ilmu matematika adalah Gottfried Wilhelm Leibniz, atau
lebih dikenal dengan sebutan Leibniz .
APLIKASI INTEGRAL
• Pada bidang matematika dan teknik untuk menghitung volume benda
putar dan luasan pada kurva.
• Pada bidang fisika untuk menghitung dan menganalisis rangkaian arus
listrik, medan magnet, dan lainnya.
• Dalam bidang ekonomi, untuk menentukan persamaan dan fungsi yang
berkaitan dengan ekonomi, konsumsi, marginal, dan sebagainya.
MACAM INTEGRAL
Integral dibedakan menjadi dua
• Integral tak tentu integral sebagai invers (kebalikan) dari turunan
• Integral tentu jumlahan suatu daerah yang dibatasi kurva atau
persamaan tertentu.
RUMUS DASAR INTEGRAL
• 𝑑𝑥 = 𝑥 + 𝐶
• 𝑎 𝑑𝑥 = 𝑎𝑥 + 𝐶
• 𝑘 𝑑𝑥 = 𝑘𝑥 + 𝐶
• 𝑥𝑛
𝑑𝑥 =
1
𝑛+1
𝑥𝑛+1
+ 𝐶 n≠ -1
• 𝑘 𝑥𝑛
𝑑𝑥 =
𝑘
𝑛+1
𝑥𝑛+1
+ 𝐶
CONTOH
1. 𝑥 𝑑𝑥 = … … …
Jawab :
𝑥 𝑑𝑥 =
1
𝑛+1
𝑥𝑛+1 + C =
2. 3 𝑑𝑥 = …
•
• (2 𝑥2
+ 5)𝑑𝑥 =
Pertemuan 1
Pertemuan 1
Pertemuan 1

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Pertemuan 1

  • 1. KALKULUS 2 by: Teti Desyani, M.Kom. PERTEMUAN 1 PENGANTAR INTEGRAL
  • 2. DESKRIPSI • Integral merupakan anti turunan atau kebalikan dari turunan. • Notasi integral : • tokoh yang mengembangkan dan memperkenalkan konsep differensial dan anti- differensial (integral) dalam ilmu matematika adalah Gottfried Wilhelm Leibniz, atau lebih dikenal dengan sebutan Leibniz .
  • 3. APLIKASI INTEGRAL • Pada bidang matematika dan teknik untuk menghitung volume benda putar dan luasan pada kurva. • Pada bidang fisika untuk menghitung dan menganalisis rangkaian arus listrik, medan magnet, dan lainnya. • Dalam bidang ekonomi, untuk menentukan persamaan dan fungsi yang berkaitan dengan ekonomi, konsumsi, marginal, dan sebagainya.
  • 4. MACAM INTEGRAL Integral dibedakan menjadi dua • Integral tak tentu integral sebagai invers (kebalikan) dari turunan • Integral tentu jumlahan suatu daerah yang dibatasi kurva atau persamaan tertentu.
  • 5. RUMUS DASAR INTEGRAL • 𝑑𝑥 = 𝑥 + 𝐶 • 𝑎 𝑑𝑥 = 𝑎𝑥 + 𝐶 • 𝑘 𝑑𝑥 = 𝑘𝑥 + 𝐶 • 𝑥𝑛 𝑑𝑥 = 1 𝑛+1 𝑥𝑛+1 + 𝐶 n≠ -1 • 𝑘 𝑥𝑛 𝑑𝑥 = 𝑘 𝑛+1 𝑥𝑛+1 + 𝐶
  • 6. CONTOH 1. 𝑥 𝑑𝑥 = … … … Jawab : 𝑥 𝑑𝑥 = 1 𝑛+1 𝑥𝑛+1 + C = 2. 3 𝑑𝑥 = …
  • 7.
  • 8.
  • 9. • (2 𝑥2 + 5)𝑑𝑥 =