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Beliebt Rechnen >

fläche x+6y=8,x+8=y^2

Lösung

fläche

x + 6 y = 8, x + 8 = y^{2}

Lösung

\frac{500}{3}

+1

Dezimale

166.66666 \dots

Schritte zur Lösung

Stelle

y

nach

x + 6 y = 8

um:

y = \frac{8 - x}{6}

Stelle

y

nach

x + 8 = y^{2}

um:

y = x + 8, y = - x + 8

f_{1} (x) = \frac{8 - x}{6}

f_{2} (x) = x + 8

Um die Schnittpunkte zu finden, löse

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

\frac{8 - x}{6} = x + 8 : x = - 4

\frac{8 - x}{6} = - x + 8 : x = 56

x + 8 = - x + 8 : x = - 8

= \int_{- 8}^{- 4} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{- 4}^{56} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 8}^{- 4} x + 8 - (- x + 8) d x + \int_{- 4}^{56} \frac{8 - x}{6} - (- x + 8) d x

\int_{- 8}^{- 4} x + 8 - (- x + 8) d x = \frac{32}{3}

\int_{- 4}^{56} \frac{8 - x}{6} - (- x + 8) d x = 156

= \frac{32}{3} + 156

Vereinfache

= \frac{500}{3}

Graph

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