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Beliebt Rechnen >

fläche x+2y=2,y-x=1,2x+y=7

Lösung

fläche

x + 2 y = 2, y - x = 1, 2 x + y = 7

Lösung

6

Schritte zur Lösung

Stelle

y

nach

x + 2 y = 2

um:

y = \frac{2 - x}{2}

Stelle

y

nach

y - x = 1

um:

y = 1 + x

Stelle

y

nach

2 x + y = 7

um:

y = 7 - 2 x

f_{1} (x) = \frac{2 - x}{2}

f_{2} (x) = 1 + x

Um die Schnittpunkte zu finden, löse

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

\frac{2 - x}{2} = 1 + x : x = 0

\frac{2 - x}{2} = 7 - 2 x : x = 4

1 + x = 7 - 2 x : x = 2

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

= \int_{0}^{2} \frac{2 - x}{2} - (1 + x) d x + \int_{2}^{4} \frac{2 - x}{2} - (7 - 2 x) d x

\int_{0}^{2} \frac{2 - x}{2} - (1 + x) d x = 3

\int_{2}^{4} \frac{2 - x}{2} - (7 - 2 x) d x = 3

= 3 + 3

Vereinfache

= 6

Graph

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