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II. Integration – 3. Generelle områder 216 3.23. Type II ☞ [S] 12.3 Double integrals over general regions Eksempel 3 - fortsat 4 y+1 xy dA = D 1 −2 2 y2 xy dx dy −3 4 1 = 2 x2 x=y+1 y = = −2 4 (− 1 x= 1 2 y2 dy −3 −2 8 y5 + 2y 3 + y 2 − 4y)dy − 1 48 y6 + 1 2 y4 + 1 3 y3 − 2y 2 4 = 36 3.24. Volumen af hjørne ☞ [S] 12.3 Double integrals over general regions Hjørne (Se også eksempel 4) Givet trekanten D = {(x,y)|0 ≤ x ≤ a,0 ≤ y ≤ b − b a x} Et hjørne med kantlængder a,b,c > 0 er givet ved E = {(x,y,z)|(x,y) ∈ D,0 ≤ z ≤ c − c c x − a b y} −2
II. Integration – 3. Generelle områder 217 Vis at volumenet V = abc 6 3.25. Hjørne ☞ [S] 12.3 Double integrals over general regions Hjørne - figur z x a D = {(x,y)|0 ≤ x ≤ a,0 ≤ y ≤ b − b a x} c E = {(x,y,z)|(x,y) ∈ D,0 ≤ z ≤ c − c c x − a b y} 3.26. Volumen af hjørne ☞ [S] 12.3 Double integrals over general regions b y
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CALCULUS "SLIDES" TIL CALCULUS 1 +
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3. Generelle områder 201 4. Koordi
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Forord "Slides" til forelæsningern
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