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Beliebt Rechnen >

fläche y=7x^2,y^2= 1/7 x

Lösung

fläche

y = 7 x^{2}, y^{2} = \frac{1}{7} x

Lösung

\frac{1}{147}

+1

Dezimale

0.00680 \dots

Schritte zur Lösung

Stelle

y

nach

y^{2} = \frac{1}{7} x

um:

y = \frac{x}{7}, y = - \frac{x}{7}

f_{1} (x) = 7 x^{2}

f_{2} (x) = \frac{x}{7}

Um die Schnittpunkte zu finden, löse

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

7 x^{2} = \frac{x}{7} : x = 0, x = \frac{1}{7}

7 x^{2} = - \frac{x}{7} : x = 0

\frac{x}{7} = - \frac{x}{7} : x = 0

= \int_{0}^{\frac{1}{7}} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{0}^{\frac{1}{7}} 7 x^{2} - \frac{x}{7} d x

\int_{0}^{\frac{1}{7}} 7 x^{2} - \frac{x}{7} d x = \frac{1}{147}

= \frac{1}{147}

Graph

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