fläche sqrt(x), 1/2 x,9

Lösung

fläche

x, \frac{1}{2} x, 9

\frac{494}{3}

Dezimale

164.66666 \dots

Schritte zur Lösung

Um die Schnittpunkte zu finden, löse

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

x = \frac{1}{2} x : x = 4, x = 0

x = 9 : x = 81

\frac{1}{2} x = 9 : x = 18

= \int_{0}^{4} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{4}^{18} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{18}^{81} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{0}^{4} x - \frac{1}{2} x d x + \int_{4}^{18} x - \frac{1}{2} x d x + \int_{18}^{81} x - 9 d x

\int_{0}^{4} x - \frac{1}{2} x d x = \frac{4}{3}

\int_{4}^{18} x - \frac{1}{2} x d x = - 362 + \frac{247}{3}

\int_{18}^{81} x - 9 d x = 81 + 362

= \frac{4}{3} - 362 + \frac{247}{3} + 81 + 362

Vereinfache

= \frac{494}{3}

x \to - 1 + lim (2 x^{3} - 2 m)

d er i v a t i v e f (x) = 5 e^{2 x}

\frac{d y}{d x} = \frac{e ^{x}}{8 + e ^{x}}

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

\int_{0}^{5} \frac{1}{x ^{\frac{14}{15}}} d x