INTEGRAL LUAS PERMUKAAN.pptx
Transcript of INTEGRAL LUAS PERMUKAAN.pptx
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INTEGRAL LUAS PERMUKAAN
Oleh :Evelyn Raflesia (14-065)Caroline (14-083)Muhammad Fachrowi (14-084)
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Integral Permukaan
Defenisi : Misalkan S bagian dari permukaan z = f (x, y) dimana (x,y) berada dalam D pada bidang XY . Jika f mmpunyai turunan parsial orde pertama yang kontinu dan g(x, y,z) = g(x, y, f (x, y))kontinu pada D , maka Integral Permukaan dari g(x, y,z) pada S adalah: ∫∫ = S g x,( y,z) dS g x y f x y f f dA D ∫∫ ,,( ,( )) x + y +1 2 2 Dimana dS adalah elemen diferensial luas permukaan
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Integral luas permukaan
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Contoh integral luas permukaan
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Integral Permukaan Medan Vektor
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Aplikasi Integral Luas Permukaan
Luas Permukaan Jika g(x, y,z) =1 , maka ∫∫ S dS adalah luas permukaan. b. Massa = m Jika rapat massa diketahui ρ(x, y,z) maka m= ∫∫ S ρ x y,,( z)dS
Contoh: Hitunglah ∫∫ + S ( dimana S bagian dari permukaan xy 2z)dS 2x + y + 3z = 6.
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Terlihat seperti gambar di bawah ini, maka penyelesaiaannya adalah
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Fluks Medan Vektor yang Melalui Permukaan
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Teorema Divergensi Gauss
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Contoh 1
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Contoh 2