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Beliebt Rechnen >

fläche x=y^2-8,x=2y

Lösung

fläche

x = y^{2} - 8, x = 2 y

Lösung

36

Schritte zur Lösung

Stelle

y

nach

x = y^{2} - 8

um:

y = x + 8, y = - x + 8

Stelle

y

nach

x = 2 y

um:

y = \frac{x}{2}

f_{1} (x) = x + 8

f_{2} (x) = - x + 8

Um die Schnittpunkte zu finden, löse

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

x + 8 = - x + 8 : x = - 8

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

- x + 8 = \frac{x}{2} : x = - 4

= \int_{- 8}^{- 4} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{- 4}^{8} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 8}^{- 4} x + 8 - (- x + 8) d x + \int_{- 4}^{8} x + 8 - \frac{x}{2} d x

\int_{- 8}^{- 4} x + 8 - (- x + 8) d x = \frac{32}{3}

\int_{- 4}^{8} x + 8 - \frac{x}{2} d x = \frac{76}{3}

= \frac{32}{3} + \frac{76}{3}

Vereinfache

= 36

Graph

Beliebte Beispiele

derivative of (x-3/x+ln(x/3))

\frac{d}{d x} (\frac{x - 3}{x} + ln (\frac{x}{3}))

limit as x approaches infinity of 3ln(x)

x \to \infty lim (3 ln (x))

d er i v a t i v e k

(\partial)/(\partial y)(e^{x+y+1})

\frac{\partial}{\partial y} (e^{x + y + 1})

integral from 0 to 1 of x-x^2

\int_{0}^{1} x - x^{2} d x