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Beliebt Rechnen >

fläche x=y^2+4y-22,x=3y+8

Lösung

fläche

x = y^{2} + 4 y - 22, x = 3 y + 8

Lösung

\frac{1331}{6}

+1

Dezimale

221.83333 \dots

Schritte zur Lösung

Stelle

y

nach

x = y^{2} + 4 y - 22

um:

y = - 2 + x + 26, y = - x + 26 - 2

Stelle

y

nach

x = 3 y + 8

um:

y = \frac{x - 8}{3}

f_{1} (x) = - 2 + x + 26

f_{2} (x) = - x + 26 - 2

Um die Schnittpunkte zu finden, löse

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

- 2 + x + 26 = - x + 26 - 2 : x = - 26

- 2 + x + 26 = \frac{x - 8}{3} : x = 23

- x + 26 - 2 = \frac{x - 8}{3} : x = - 10

= \int_{- 26}^{- 10} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{- 10}^{23} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 26}^{- 10} - 2 + x + 26 - (- x + 26 - 2) d x + \int_{- 10}^{23} - 2 + x + 26 - \frac{x - 8}{3} d x

\int_{- 26}^{- 10} - 2 + x + 26 - (- x + 26 - 2) d x = \frac{256}{3}

\int_{- 10}^{23} - 2 + x + 26 - \frac{x - 8}{3} d x = \frac{273}{2}

= \frac{256}{3} + \frac{273}{2}

Vereinfache

= \frac{1331}{6}

Graph

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