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Beliebt Rechnen >

fläche x=y^2,x=2-y

Lösung

fläche

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

Lösung

\frac{9}{2}

+1

Dezimale

4.5

Schritte zur Lösung

Stelle

y

nach

x = y^{2}

um:

y = x, y = - x

Stelle

y

nach

x = 2 - y

um:

y = 2 - x

f_{1} (x) = x

f_{2} (x) = - x

Um die Schnittpunkte zu finden, löse

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

x = - x : x = 0

x = 2 - x : x = 1

- x = 2 - x : x = 4

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

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

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

\int_{1}^{4} - x - (2 - x) d x = \frac{19}{6}

= \frac{4}{3} + \frac{19}{6}

Vereinfache

= \frac{9}{2}

Graph

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