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Beliebt Rechnen >

fläche x=y^2-12,x=4y

Lösung

fläche

x = y^{2} - 12, x = 4 y

Lösung

\frac{256}{3}

+1

Dezimale

85.33333 \dots

Schritte zur Lösung

Stelle

y

nach

x = y^{2} - 12

um:

y = x + 12, y = - x + 12

Stelle

y

nach

x = 4 y

um:

y = \frac{x}{4}

f_{1} (x) = x + 12

f_{2} (x) = - x + 12

Um die Schnittpunkte zu finden, löse

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

x + 12 = - x + 12 : x = - 12

x + 12 = \frac{x}{4} : x = 24

- x + 12 = \frac{x}{4} : x = - 8

= \int_{- 12}^{- 8} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{- 8}^{24} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 12}^{- 8} x + 12 - (- x + 12) d x + \int_{- 8}^{24} x + 12 - \frac{x}{4} d x

\int_{- 12}^{- 8} x + 12 - (- x + 12) d x = \frac{32}{3}

\int_{- 8}^{24} x + 12 - \frac{x}{4} d x = \frac{224}{3}

= \frac{32}{3} + \frac{224}{3}

Vereinfache

= \frac{256}{3}

Graph

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