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Beliebt Rechnen >

fläche x=4y,x=y^2-5

Lösung

fläche

x = 4 y, x = y^{2} - 5

Lösung

36

Schritte zur Lösung

Stelle

y

nach

x = 4 y

um:

y = \frac{x}{4}

Stelle

y

nach

x = y^{2} - 5

um:

y = x + 5, y = - x + 5

f_{1} (x) = \frac{x}{4}

f_{2} (x) = x + 5

Um die Schnittpunkte zu finden, löse

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

\frac{x}{4} = x + 5 : x = 20

\frac{x}{4} = - x + 5 : x = - 4

x + 5 = - x + 5 : x = - 5

= \int_{- 5}^{- 4} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{- 4}^{20} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{- 5}^{- 4} x + 5 - (- x + 5) d x + \int_{- 4}^{20} \frac{x}{4} - x + 5 d x

\int_{- 5}^{- 4} x + 5 - (- x + 5) d x = \frac{4}{3}

\int_{- 4}^{20} \frac{x}{4} - x + 5 d x = \frac{104}{3}

= \frac{4}{3} + \frac{104}{3}

Vereinfache

= 36

Graph

Beliebte Beispiele

integral from-4 to 4 of (2x^7+1)

\int_{- 4}^{4} (2 x^{7} + 1) d x

derivative (1/(y^2)-9/(y^4))(y+3y^3)

d er i v a t i v e (\frac{1}{y ^{2}} - \frac{9}{y ^{4}}) (y + 3 y^{3})

integral from 2 to 4 of f(x)

\int_{2}^{4} f (x) d x

f^{^{'}} (x) = \frac{4}{x}

integral of 1/(sqrt(36x^2+2))

\int \frac{1}{36 x ^{2} + 2} d x