Flächeninhalt zwischen Funktionsgraphen Integralrechnung ★ Übung mit Lösung

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Situation: Die folgende Graphik zeigt die Erlös- und Kostensituation der GmbH für das Produkt „SoundCube“ bezüglich der letzten Jahre. • Kannst du noch…? • Bestimmte Integrale • Orientierter und tatsächlicher Flächeninhalt • Übung 1: Erstellen Sie eine 5-Jahresauswertung zu dem Produkt „SoundCube“, um im Team zu entscheiden, ob die letzten 5 Jahre als ‚erfolgreich‘ oder ‚nicht erfolgreich‘ bezeichnet werden können. • Bestimmen Sie die Koordinaten der Schnittpunkte von E(x) mit K(x). • Berechnen Sie den Gesamtgewinn der GmbH in den ersten fünf Jahren mit dem Produkt. • Berechnen Sie den Gesamtverlust der GmbH in den ersten fünf Jahren mit dem Produkt. • Wie schätzen Sie die wirtschaftliche Gesamtsituation des Produkts „SoundCube“ aus Sicht der QuickTel GmbH ein? • Übung 2: • Ermitteln Sie rechnerisch die Maßzahl der Fläche, die von f(x)=2x²-x+2.5 und g(x)=x+2.5 eingeschlossen wird und überprüfen Sie mit dem GTR. • Übung 3: • Berechnen Sie die Maßzahl I der der gesamten, eingeschlossenen Fläche mit Hilfe der Differenzfunktion. • Füllen Sie die Graphik soweit es geht aus und überprüfen Sie auch mit dem GTR. • • Was du jetzt kannst! • Ich kann Flächen zwischen Funktionsgraphen berechnen, indem ich die Fläche unter einem höher liegenden Graphen minus die Fläche unter dem niedriger liegenden Graphen berechne (bezüglich eines Intervalls). • Ich weiß, dass ich zur Berechnung von „schwierigen“ Flächen zwischen Graphen, die Differenzfunktion verwenden 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