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Beliebt Rechnen >

fläche x=y^4,x=y^5

Lösung

fläche

x = y^{4}, x = y^{5}

Lösung

\frac{1}{30}

+1

Dezimale

0.03333 \dots

Schritte zur Lösung

Stelle

y

nach

x = y^{4}

um:

y = 4 x, y = - 4 x

Stelle

y

nach

x = y^{5}

um:

y = 5 x

f_{1} (x) = 4 x

f_{2} (x) = - 4 x

Um die Schnittpunkte zu finden, löse

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

4 x = - 4 x : x = 0

4 x = 5 x : x = 0, x = 1

- 4 x = 5 x : x = 0

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

= \int_{0}^{1} 4 x - 5 x d x

\int_{0}^{1} 4 x - 5 x d x = \frac{1}{30}

= \frac{1}{30}

Graph

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