fläche 1/(18x^2),x, x/8

Lösung

fläche

\frac{1}{18 x ^{2}}, x, \frac{x}{8}

\frac{7 3 18}{288} + \frac{4 3 18 + 3 2 \cdot 3 ^{\frac{2}{3}}}{288}

Dezimale

0.10919 \dots

Schritte zur Lösung

Um die Schnittpunkte zu finden, löse

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

\frac{1}{18 x ^{2}} = x : x = \frac{1}{3 18}

\frac{1}{18 x ^{2}} = \frac{x}{8} : x = 3 \frac{4}{9}

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

= \int_{0}^{\frac{1}{3 18}} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{\frac{1}{3 18}}^{3 \frac{4}{9}} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{0}^{\frac{1}{3 18}} x - \frac{x}{8} d x + \int_{\frac{1}{3 18}}^{3 \frac{4}{9}} \frac{1}{18 x ^{2}} - \frac{x}{8} d x

\int_{0}^{\frac{1}{3 18}} x - \frac{x}{8} d x = \frac{7}{16 \cdot 1 8 ^{\frac{2}{3}}}

\int_{\frac{1}{3 18}}^{3 \frac{4}{9}} \frac{1}{18 x ^{2}} - \frac{x}{8} d x = \frac{- 8 \cdot 1 8 ^{\frac{2}{3}} 3 \frac{9}{4} + 54 \cdot 2 ^{\frac{2}{3}} 3 2 + 3 \cdot 3 ^{\frac{2}{3}} 3 3}{144 \cdot 1 8 ^{\frac{2}{3}}}

= \frac{7}{16 \cdot 1 8 ^{\frac{2}{3}}} + \frac{- 8 \cdot 1 8 ^{\frac{2}{3}} 3 \frac{9}{4} + 54 \cdot 2 ^{\frac{2}{3}} 3 2 + 3 \cdot 3 ^{\frac{2}{3}} 3 3}{144 \cdot 1 8 ^{\frac{2}{3}}}

Vereinfache

= \frac{7 3 18}{288} + \frac{4 3 18 + 3 2 \cdot 3 ^{\frac{2}{3}}}{288}

\frac{d ^{2}}{d x ^{2}} (e^{- 6 x})

t an g e n t f (x) = 3 e^{x} cos (x), at x = 0

\frac{\partial}{\partial x} (x^{2} + \frac{y}{x})

\frac{d}{d x} (\frac{11 x}{( x ^{2} + 1 ) ^{\frac{3}{5}}})

d er i v a t i v e \frac{x}{x + 1}