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II. Integration – 4. Koordinatskift 240 Dobbelt integralet beregnes ved koordinatskift π/2 V = f(x,y)dA = R −π/2 2 cos θ 0 r 2 rdr dθ 4.26. Polær Type II, eksempel ☞ [S] 12.4 Double integrals in polar . . . Eksempel 3 - fortsat π/2 2 cos θ V = r 2 rdr dθ −π/2 π/2 4 r = −π/2 4 r=0 π/2 = 4cos 4 θ dθ = ... = 3π 2 −π/2 0 r=2 cos θ 4.27. Kilen ☞ [S] 12.4 Double integrals in polar . . . Kile dθ
II. Integration – 4. Koordinatskift 241 Kilen med radius a og højde b er i "cylinderkoordinater": Vis, at volumenet V er D = {(r,θ)|0 ≤ r ≤ a,0 ≤ θ ≤ π} E = {(r,θ,z)|(r,θ) ∈ D,0 ≤ z ≤ b r sin θ} a V = 2 3 a2 b 4.28. Kile i polære koordinater ☞ [S] 12.4 Double integrals in polar . . . Kile - figur z x a D = {(r,θ)|0 ≤ r ≤ a,0 ≤ θ ≤ π} b a y
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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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0-række/søjle, 423 n-te afsnitssu
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Identitetsmatricen, 383 Identitetsm
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