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II. Integration – 1. Dobbelt integral 180 1.28. Brug regneregler ☞ [S] 12.1 Double integrals over rectangles Opgave Lad R = [0,1] × [0,1]. Afgør om xy dA ≥ x R R 2 y 2 dA Løsning For 0 ≤ x,y ≤ 1 er så uligheden er sand ifølge regneregel 9 . xy ≥ x 2 y 2 1.29. Brug regneregler ☞ [S] 12.1 Double integrals over rectangles Opgave Lad R = [0,2] × [0,2]. Afgør om (x + y)dA ≤ 16 Løsning For 0 ≤ x,y ≤ 2 er x + y ≤ 4 R
II. Integration – 1. Dobbelt integral 181 så ifølge regneregel 9 R (x + y)dA ≤ R 4dA ≤ 16 1.30. Test integral regneregler ☞ [S] 12.1 Double integrals over rectangles Test Lad f(x,y) = xy, R = [1,2] × [1,2]. For integralet V = xy dA gælder uligheder R (a) 1 ≤ V ≤ 4. (b) 4 < V . (c) V < 1. (a) (b) (c) Afkryds den rigtige: Løsning For (x,y) ∈ R gælder uligheden 1 ≤ f(x,y) ≤ 4 Heraf, A(R) = (2 − 1)(2 − 1) = 1, A(R) ≤ V ≤ A(R) · 4 1.31. Regneregler og volumen ☞ [S] 12.1 Double integrals over rectangles Eksempel
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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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