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Beliebt Rechnen >

fläche x+y^2=6,x+y=0

Lösung

fläche

x + y^{2} = 6, x + y = 0

Lösung

\frac{125}{6}

+1

Dezimale

20.83333 \dots

Schritte zur Lösung

Stelle

y

nach

x + y^{2} = 6

um:

y = 6 - x, y = - 6 - x

Stelle

y

nach

x + y = 0

um:

y = - x

f_{1} (x) = 6 - x

f_{2} (x) = - 6 - x

Um die Schnittpunkte zu finden, löse

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

6 - x = - 6 - x : x = 6

6 - x = - x : x = - 3

- 6 - x = - x : x = 2

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

= \int_{- 3}^{2} 6 - x - (- x) d x + \int_{2}^{6} - 6 - x - 6 - x d x

\int_{- 3}^{2} 6 - x - (- x) d x = \frac{61}{6}

\int_{2}^{6} - 6 - x - 6 - x d x = \frac{32}{3}

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

Vereinfache

= \frac{125}{6}

Graph

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