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Beliebt Rechnen >

fläche x=2y,x+1=(y-1)^2

Lösung

fläche

x = 2 y, x + 1 = (y - 1)^{2}

Lösung

\frac{32}{3}

+1

Dezimale

10.66666 \dots

Schritte zur Lösung

Stelle

y

nach

x = 2 y

um:

y = \frac{x}{2}

Stelle

y

nach

x + 1 = (y - 1)^{2}

um:

y = x + 1 + 1, y = - x + 1 + 1

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

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

Um die Schnittpunkte zu finden, löse

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

\frac{x}{2} = x + 1 + 1 : x = 8

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

x + 1 + 1 = - x + 1 + 1 : x = - 1

= \int_{- 1}^{0} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{0}^{8} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{- 1}^{0} x + 1 + 1 - (- x + 1 + 1) d x + \int_{0}^{8} \frac{x}{2} - (x + 1 + 1) d x

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

\int_{0}^{8} \frac{x}{2} - (x + 1 + 1) d x = \frac{28}{3}

= \frac{4}{3} + \frac{28}{3}

Vereinfache

= \frac{32}{3}

Graph

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