fläche y= 2/x ,y=8x,y= 1/2 x

Lösung

fläche

y = \frac{2}{x}, y = 8 x, y = \frac{1}{2} x

8 ln (2)

Dezimale

5.54517 \dots

Schritte zur Lösung

Um die Schnittpunkte zu finden, löse

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

\frac{2}{x} = 8 x : x = \frac{1}{2}, x = - \frac{1}{2}

\frac{2}{x} = \frac{1}{2} x : x = 2, x = - 2

8 x = \frac{1}{2} x : x = 0

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

= \int_{- 2}^{- \frac{1}{2}} \frac{2}{x} - \frac{1}{2} x d x + \int_{- \frac{1}{2}}^{0} \frac{1}{2} x - 8 x d x + \int_{0}^{\frac{1}{2}} 8 x - \frac{1}{2} x d x + \int_{\frac{1}{2}}^{2} \frac{2}{x} - \frac{1}{2} x d x

\int_{- 2}^{- \frac{1}{2}} \frac{2}{x} - \frac{1}{2} x d x = 4 ln (2) - \frac{15}{16}

\int_{- \frac{1}{2}}^{0} \frac{1}{2} x - 8 x d x = \frac{15}{16}

\int_{0}^{\frac{1}{2}} 8 x - \frac{1}{2} x d x = \frac{15}{16}

\int_{\frac{1}{2}}^{2} \frac{2}{x} - \frac{1}{2} x d x = 4 ln (2) - \frac{15}{16}

= 4 ln (2) - \frac{15}{16} + \frac{15}{16} + \frac{15}{16} + 4 ln (2) - \frac{15}{16}

Vereinfache

= 8 ln (2)

\frac{d}{d x} (\frac{3}{4 ( 2 x - 5 ) ^{8}})

x \to - \infty lim (\frac{x ^{2} + 8 x}{8 x + 1})

d er i v a t i v e f (x) = 2000 (x^{2} + 5)^{\frac{1}{3}}

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

\frac{d}{d x} (4 x^{3} - 10 x^{2})