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II. Integration – 4. Koordinatskift 236 Eksempel 2 - fortsat Volumenet er et integral af funktionen på cirkelskiven Dobbelt integralet beregnes ved koordinatskift V = f(x,y)dA = R f(x,y) = 1 − x 2 − y 2 R = {(x,y)|x 2 + y 2 ≤ 1} 2π 1 0 0 (1 − r 2 )rdr dθ 4.20. Integral over en cirkelskive ☞ [S] 12.4 Double integrals in polar . . . Eksempel 2 - fortsat V = = = 2π 1 0 2π 0 2π 0 = π 2 0 r 2 2 1 4 dθ (1 − r 2 )rdr dθ r=1 r4 − dθ 4 r=0
II. Integration – 4. Koordinatskift 237 4.21. Polært Type II ☞ [S] 12.4 Double integrals in polar coordinates Type II - figur = y = r=h1( ) r=h2( ) D = {(r,θ)|α ≤ θ ≤ β, h1(θ) ≤ r ≤ h2(θ)} 4.22. Polær Type II ☞ [S] 12.3 Double integrals over general regions Polœr Type II integral 3 For f givet på D = {(r,θ)|α ≤ θ ≤ β, h1(θ) ≤ r ≤ h2(θ)} x
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CALCULUS "SLIDES" TIL CALCULUS 1 +
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3. Generelle områder 201 4. Koordi
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V. Matricer - 4. Determinanter = (
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