fläche y=x-6,y^2=x

Lösung

fläche

y = x - 6, y^{2} = x

\frac{125}{6}

Dezimale

20.83333 \dots

Schritte zur Lösung

Stelle

y

nach

y^{2} = x

um:

y = x, y = - x

f_{1} (x) = x - 6

f_{2} (x) = x

Um die Schnittpunkte zu finden, löse

f_{i} (x) = f_{j} (x)

x - 6 = x : x = 9

x - 6 = - x : x = 4

x = - x : x = 0

= \int_{0}^{4} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{4}^{9} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{0}^{4} x - (- x) d x + \int_{4}^{9} x - 6 - x d x

\int_{0}^{4} x - (- x) d x = \frac{32}{3}

\int_{4}^{9} x - 6 - x d x = \frac{61}{6}

= \frac{32}{3} + \frac{61}{6}

Vereinfache

= \frac{125}{6}

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