Maj 2008 (udvalgte opgaver)Alternativ besvarelse p\303\245 udvalgte dele af opgaverne.Opgave 31)Graf og 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Jacobi-funktionen er 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integrant-udtrykket er 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)Fladens masseVed brug af standard-metoden f\303\245s: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 brug af Integrator8-pakken: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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2KVEpc2ltcGxpZnlGJy8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUlYm9sZEdRJmZhbHNlRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNigtRiM2KC1GLDYpUSIlRidGL0YyRjVGOEY7Rj1GL0YyRjhGOy9GPlEnbm9ybWFsRidGL0YyRjhGO0ZILUYsNiNRIUYnRi9GMkY4RjtGSA==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEmZXZhbGZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYmUSIlRidGLy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRjJGPS9GM1Enbm9ybWFsRidGQC1GLDYjUSFGJ0Y9RkA=Bem\303\246rk, at Maple/Integrator8 ikke kan bestemme dette integral eksakt!Det skyldes, at Maple ikke kender den trigonometriske formel for dobbelt vinkel: 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kurveintegral af VCirkel C1:Oml\303\270bsretning imod uret i 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C2:Oml\303\270bsretning med uret i 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det tangentielle kurveintegral af V langs LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y1RkE= er 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, og det tangentielle kurveintegral af V langs LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y1RkE= er 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)Flux af W gennem 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vha. 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