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Beliebt Rechnen >

fläche x+y^2=30,x+y=0

Lösung

fläche

x + y^{2} = 30, x + y = 0

Lösung

\frac{1331}{6}

+1

Dezimale

221.83333 \dots

Schritte zur Lösung

Stelle

y

nach

x + y^{2} = 30

um:

y = 30 - x, y = - 30 - x

Stelle

y

nach

x + y = 0

um:

y = - x

f_{1} (x) = 30 - x

f_{2} (x) = - 30 - x

Um die Schnittpunkte zu finden, löse

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

30 - x = - 30 - x : x = 30

30 - x = - x : x = - 6

- 30 - x = - x : x = 5

= \int_{- 6}^{5} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{5}^{30} ∣ f_{2} (x) - f_{1} (x) ∣ d x

= \int_{- 6}^{5} 30 - x - (- x) d x + \int_{5}^{30} - 30 - x - 30 - x d x

\int_{- 6}^{5} 30 - x - (- x) d x = \frac{331}{6}

\int_{5}^{30} - 30 - x - 30 - x d x = \frac{500}{3}

= \frac{331}{6} + \frac{500}{3}

Vereinfache

= \frac{1331}{6}

Graph

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