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Pertemuan 7 Integral - INTEGRAL Materi Konsep Integral...

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INTEGRAL
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Materi Konsep Integral Integral Tak Tentu Rumus Dasar Integral Integrasi Tertentu Integrasi Parsial Berbagai Metoda Integrasi – Integration by part – Metoda substitusi – Integrasi pecahan rasional
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Materi Penggunaan Integral – Luas Daerah Bidang Rata – Volume Benda dalam Ruang Lempengan, Cakram, Cincin – Volume Benda Putar – Panjang Kurva pada Bidang – Kerja
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Integral adalah kebalikan dari diferensial 3 2 ( 5) 3 d x x dx + = 2 3 3 x dx x C = + 2 3 3 x dx x C = + Konstanta integral (C) harus selalu dicantum- kan dalam suatu hasil integrasi suatu fungsi
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( ) ( ) dF x f x dx = Maka fungsi F(x) dapat diperoleh kembali dengan integrasi: ( ) ( ) F x f x dx C = + Karena nilai C dapat sembarang, maka F(x) disebut integral tak tentu dari f(x).
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( ) ( ) ( ) x b x a f x dx F b F a = = = Jika fungsi f(x) adalah suatu fungsi kontinyu dalam interval x=a dan x=b, maka x=a Æ batas bawah integrasi x=b Æ batas atas integrasi Integral Tertentu
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6 (5 4) x dx 6 x dx mirip Penyelesaian, dimisalkan (5x-4) = z 1 1 5 dx dz dz dx = = Æ dimana: dx z dx z dz dz =
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6 6 7 1 1 1 5 5 7 z dx z dz z C = = + 6 7 1 (5 4) (5 4) 35 x dx x C = + cos(7 2) x dx + = 5 4 x e dx + = Coba selesaikan integrasi berikut ini:
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'( ) ( ) f x dx f x '( ) ( ) f x f x dx Integrasi dalam bentuk dan Bentuk integrasi dapat dibawa ke bentuk rumus dasar integral '( ) 1 [ ( )] ( ) ( ) f x dx d f x f x f x = '( ) ( ) ( ) [ ( )] f x f x dx f x d f x =
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2 2 2 3 ln( 3 5) 3 5 x dx x x C x x + = + + + 2 2 1 tan sec tan 2 x x dx x C = + Contoh: Coba selesaikan integrasi berikut ini: 2 3 6 2 x dx x x = + cos 1 sin x dx x = +
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