面積 1/(12x^2),x, x/(10)

解

面積

\frac{1}{12 x ^{2}}, x, \frac{x}{10}

\frac{15 \cdot 2 ^{\frac{2}{3}} 3 3 - 2 3 150 - 3 6 \cdot 5 ^{\frac{2}{3}}}{120}

十進法表記

0.15334 \dots

解答ステップ

交点を見つけるには以下を解く:

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

\frac{1}{12 x ^{2}} = x : x = \frac{1}{3 12}

\frac{1}{12 x ^{2}} = \frac{x}{10} : x = 3 \frac{5}{6}

x = \frac{x}{10} : x = 0

= \int_{0}^{\frac{1}{3 12}} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{\frac{1}{3 12}}^{3 \frac{5}{6}} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{0}^{\frac{1}{3 12}} x - \frac{x}{10} d x + \int_{\frac{1}{3 12}}^{3 \frac{5}{6}} \frac{1}{12 x ^{2}} - \frac{x}{10} d x

\int_{0}^{\frac{1}{3 12}} x - \frac{x}{10} d x = \frac{3 3 3}{40 3 2}

\int_{\frac{1}{3 12}}^{3 \frac{5}{6}} \frac{1}{12 x ^{2}} - \frac{x}{10} d x = \frac{- 4 3 450 + 20 \cdot 3 ^{\frac{2}{3}} 3 4 - 2 \cdot 1 5 ^{\frac{2}{3}} 3 2 + 6 ^{\frac{2}{3}}}{240 3 3}

= \frac{3 3 3}{40 3 2} + \frac{- 4 3 450 + 20 \cdot 3 ^{\frac{2}{3}} 3 4 - 2 \cdot 1 5 ^{\frac{2}{3}} 3 2 + 6 ^{\frac{2}{3}}}{240 3 3}

簡素化

= \frac{15 \cdot 2 ^{\frac{2}{3}} 3 3 - 2 3 150 - 3 6 \cdot 5 ^{\frac{2}{3}}}{120}