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II. Integration – 4. Koordinatskift 242 E = {(r,θ,z)|(r,θ) ∈ D,0 ≤ z ≤ b r sin θ} a 4.29. Volumen af kile ☞ [S] 12.4 Double integrals in polar . . . Kile - fortsat D = {(r,θ)|0 ≤ r ≤ a,0 ≤ θ ≤ π} er et polært rektangel. Volumenet af kilen er D π a b b y dA = r sin(θ)rdr dθ a a 0 4.30. Volumen af kile ☞ [S] [S] 12.4 Double integrals in polar . . . Kile - fortsat π a b b y dA = r sin(θ)rdr dθ D a 0 0 a π b = 0 3a r3 r=a sinθ dθ r=0 π a = 0 2b sinθ dθ 3 = a2b [−cos θ]π 0 3 0
II. Integration – 4. Koordinatskift 243 = 2 3 a2 b 4.31. Opgave ☞ Matematik Alfa 1, August 2002 Opgave 1 Lad R betegne kvartcirkelskiven x2 + y2 ≤ 4, x ≥ 0,y ≥ 0. (Tegn.) Udregn R x2y dA. Løsning y R = {(x,y)|0 ≤ x,0 ≤ y,x 2 + y 2 ≤ 4} 4.32. Opgave ☞ Matematik Alfa 1, August 2002 Opgave 1 - figur 2 x
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CALCULUS "SLIDES" TIL CALCULUS 1 +
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3. Generelle områder 201 4. Koordi
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Litteratur • Arnold, Ordinary dif
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