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II. Integration – 2. Itereret integral 190 2.13. Test itereret integral ☞ [S] 12.2 Iterated integrals Test Lad f(x,y) = xy. Det itererede integral 2 2 xy dxdy er 1 1 (a) 9 2 . (b) 9 4 Løsning . (c) 6 4 . 2 2 1 1 2 2 x xy dxdy = 1 2 = 3 2 2 y 2 2 1 = 3 3 9 = 2 2 4 x=2 Afkryds den rigtige: y dy x=1 (a) (b) (c) 2.14. Øvelse gør mester ☞ [S] 12.2 Iterated integrals Eksempel R = [0,1] × [0,1], f(x,y) = 2x + 2ye x Partial integral A(x) = 1 0 (2x + 2ye x )dy
II. Integration – 2. Itereret integral 191 = 2xy + y 2 e x y=1 y=0 = 2x + e x 2.15. Videre ☞ [S] 12.2 Iterated integrals Eksempel - fortsat Itereret integral 1 1 0 0 A(x) = 2x + e x (2x + 2ye x )dydx = 1 0 (2x + e x )dx = x 2 + e x 1 0 = (1 + e) − (0 + 1) 2.16. Fortsat avet om ☞ [S] 12.2 Iterated integrals Eksempel - fortsat R = [0,1] × [0,1], f(x,y) = 2x + 2ye x = e
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CALCULUS "SLIDES" TIL CALCULUS 1 +
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3. Generelle områder 201 4. Koordi
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