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II. Integration – 4. Koordinatskift 234 Eksempel 1 - fortsat (3x + 4y R 2 π )dA = 0 1 π 3 4 2 r=2 = r cos θ + r sin θ r=1 0 dθ π = (7cos θ + 15sin 0 2 θ)dθ π = (7cos θ + 0 15 (1 − cos 2θ))dθ 2 = 7sin θ + 15 θ=π (2θ − sin 2θ) 4 θ=0 = 15 2 π 2 (3r cos θ + 4r 2 sin 2 θ)rdr dθ 4.17. Integral over en cirkelskive ☞ [S] 12.4 Double integrals in polar . . . Eksempel 2 Toppen af et æg {(x,y,z)|x 2 + y 2 ≤ 1, 0 ≤ z ≤ 1 − x 2 − y 2 } beskrives i "cylinder" koordinater ved x = r cos θ, y = r sin θ
II. Integration – 4. Koordinatskift 235 Det er {(r,θ,z)|0 ≤ r ≤ 1,0 ≤ z ≤ 1 − r 2 } 4.18. Top ☞ [S] 12.4 Double integrals in polar coordinates Eksempel 2 - figur x z {(r,θ,z)|0 ≤ r ≤ 1,0 ≤ z ≤ 1 − r 2 } 4.19. Integral over en cirkelskive ☞ [S] 12.4 Double integrals in polar . . . 1 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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Litteratur • Arnold, Ordinary dif
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0-række/søjle, 423 n-te afsnitssu
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