fläche y=2-x/2 ,x=2y^2

Lösung

fläche

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

9

Schritte zur Lösung

Stelle

y

nach

x = 2 y^{2}

um:

y = \frac{x}{2}, y = - \frac{x}{2}

f_{1} (x) = 2 - \frac{x}{2}

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

Um die Schnittpunkte zu finden, löse

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

2 - \frac{x}{2} = \frac{x}{2} : x = 2

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

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

= \int_{0}^{2} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{2}^{8} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{0}^{2} \frac{x}{2} - (- \frac{x}{2}) d x + \int_{2}^{8} 2 - \frac{x}{2} - (- \frac{x}{2}) d x

\int_{0}^{2} \frac{x}{2} - (- \frac{x}{2}) d x = \frac{8}{3}

\int_{2}^{8} 2 - \frac{x}{2} - (- \frac{x}{2}) d x = \frac{19}{3}

= \frac{8}{3} + \frac{19}{3}

Vereinfache

= 9

\int (9 x + 2)^{2} d x

\int \frac{a + b x ^{5}}{6 a x + b x ^{6}} d x

y^{^{''}} + 4 y^{^{'}} - 24 y = 0

\int e^{x} + e^{x} x d x

d er i v a t i v e g (x) = \frac{1}{x}