fläche 1/((16x^2)),x, x/6

Lösung

fläche

\frac{1}{( 16 x ^{2} )}, x, \frac{x}{6}

\frac{6 \cdot 3 ^{\frac{2}{3}} 3 6 - 3 2 \cdot 6 ^{\frac{2}{3}} - 4 \cdot 3 ^{\frac{2}{3}}}{96}

Dezimale

0.10622 \dots

Schritte zur Lösung

Um die Schnittpunkte zu finden, löse

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

\frac{1}{( 16 x ^{2} )} = x : x = \frac{1}{2 3 2}

\frac{1}{( 16 x ^{2} )} = \frac{x}{6} : x = \frac{3 3}{2}

x = \frac{x}{6} : x = 0

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

= \int_{0}^{\frac{1}{2 3 2}} x - \frac{x}{6} d x + \int_{\frac{1}{2 3 2}}^{\frac{3 3}{2}} \frac{1}{( 16 x ^{2} )} - \frac{x}{6} d x

\int_{0}^{\frac{1}{2 3 2}} x - \frac{x}{6} d x = \frac{5}{48 \cdot 2 ^{\frac{2}{3}}}

\int_{\frac{1}{2 3 2}}^{\frac{3 3}{2}} \frac{1}{( 16 x ^{2} )} - \frac{x}{6} d x = \frac{- 1 + 3 6}{8 3 3} - \frac{6 ^{\frac{2}{3}} - 1}{48 \cdot 2 ^{\frac{2}{3}}}

= \frac{5}{48 \cdot 2 ^{\frac{2}{3}}} + \frac{- 1 + 3 6}{8 3 3} - \frac{6 ^{\frac{2}{3}} - 1}{48 \cdot 2 ^{\frac{2}{3}}}

Vereinfache

= \frac{6 \cdot 3 ^{\frac{2}{3}} 3 6 - 3 2 \cdot 6 ^{\frac{2}{3}} - 4 \cdot 3 ^{\frac{2}{3}}}{96}

\frac{\partial}{\partial x} (x e^{4 x + 2 y})

\int \frac{1}{6 + 2 x} d x

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

n = 4 \sum \infty 3 (- \frac{1}{2})^{n}

x \to 0 lim (x^{\frac{1}{3}})