面積 y= 1/(18x^2),y=x,y= x/6

解

面積

y = \frac{1}{18 x ^{2}}, y = x, y = \frac{x}{6}

\frac{2 3 18 - 2 ^{\frac{2}{3}} 3 6}{24}

十進法表記

0.09820 \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}{18 x ^{2}} = x : x = \frac{1}{3 18}

\frac{1}{18 x ^{2}} = \frac{x}{6} : x = \frac{1}{3 3}

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

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

= \int_{0}^{\frac{1}{3 18}} x - \frac{x}{6} d x + \int_{\frac{1}{3 18}}^{\frac{1}{3 3}} \frac{1}{18 x ^{2}} - \frac{x}{6} d x

\int_{0}^{\frac{1}{3 18}} x - \frac{x}{6} d x = \frac{5}{12 \cdot 1 8 ^{\frac{2}{3}}}

\int_{\frac{1}{3 18}}^{\frac{1}{3 3}} \frac{1}{18 x ^{2}} - \frac{x}{6} d x = \frac{- 9 \cdot 2 ^{\frac{2}{3}} 3 3 + 6 \cdot 2 ^{\frac{2}{3}} 3 18 + 3 ^{\frac{2}{3}}}{108 \cdot 2 ^{\frac{2}{3}}}

= \frac{5}{12 \cdot 1 8 ^{\frac{2}{3}}} + \frac{- 9 \cdot 2 ^{\frac{2}{3}} 3 3 + 6 \cdot 2 ^{\frac{2}{3}} 3 18 + 3 ^{\frac{2}{3}}}{108 \cdot 2 ^{\frac{2}{3}}}

簡素化

= \frac{2 3 18 - 2 ^{\frac{2}{3}} 3 6}{24}