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Teknik Pengintegralan

Teknik Pengintegralan. Definisi: Integral tak tentu suatu fungsi f, ditulis: ∫ f(x) dx adalah anti turunan f yang paling umum, yaitu: ∫ f(x) dx = F(x) + c. Rumus Dasar Pengintegralan. Sifat-sifat. Pengintegralan dengan cara penggantian.

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Teknik Pengintegralan

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  1. Teknik Pengintegralan Definisi: Integral tak tentu suatu fungsi f, ditulis: ∫ f(x) dx adalah anti turunan f yang paling umum, yaitu: ∫ f(x) dx = F(x) + c

  2. Rumus Dasar Pengintegralan

  3. Sifat-sifat

  4. Pengintegralan dengan cara penggantian • Rumus dasar pengintegralan dapat diperluas untuk bermacam-macam bentuk integran memakai teknik yang dikenal sebagai penggantian. • Misalkan u = g(x) pada rumus pengintegralan ∫f(u) du = F(u) + c maka diperoleh ∫f(g(x)) d(g(x))=F(g(x)) + c

  5. Pengintegralan Parsial • Andaikan u =f(x) dan v = g(x). Diketahui bahwa: Dx[f(x) g(x)] = f(x) g’(x) + f’(x) g(x) Dengan pengintegralan kedua ruas, diperoleh: f(x) g(x) = ∫f(x) g’(x) dx + ∫g(x) f’(x) dx. Atau ∫f(x) g’(x) dx = f(x) g(x) - ∫g(x) f’(x) dx. Secara simbolis, dapat ditulis: ∫u dv = uv - ∫ v du

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