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人気のある微分積分 >

面積 x= 4/y ,x= y/8 ,x=8y

解

面積

x = \frac{4}{y}, x = \frac{y}{8}, x = 8 y

解

24 ln (2)

+1

十進法表記

16.63553 \dots

解答ステップ

以下のために

y

を分離:

x = \frac{4}{y} : y = \frac{4}{x}; x \neq = 0

以下のために

y

を分離:

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

以下のために

y

を分離:

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

f_{1} (x) = \frac{4}{x}

f_{2} (x) = 8 x

交点を見つけるには以下を解く:

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

\frac{4}{x} = 8 x : x = \frac{1}{2}, x = - \frac{1}{2}

\frac{4}{x} = \frac{x}{8} : x = 42, x = - 42

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

= \int_{- 42}^{- \frac{1}{2}} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{- \frac{1}{2}}^{0} ∣ f_{3} (x) - f_{2} (x) ∣ d x + \int_{0}^{\frac{1}{2}} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{\frac{1}{2}}^{42} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 42}^{- \frac{1}{2}} \frac{4}{x} - \frac{x}{8} d x + \int_{- \frac{1}{2}}^{0} \frac{x}{8} - 8 x d x + \int_{0}^{\frac{1}{2}} 8 x - \frac{x}{8} d x + \int_{\frac{1}{2}}^{42} \frac{4}{x} - \frac{x}{8} d x

\int_{- 42}^{- \frac{1}{2}} \frac{4}{x} - \frac{x}{8} d x = 12 ln (2) - \frac{63}{32}

\int_{- \frac{1}{2}}^{0} \frac{x}{8} - 8 x d x = \frac{63}{32}

\int_{0}^{\frac{1}{2}} 8 x - \frac{x}{8} d x = \frac{63}{32}

\int_{\frac{1}{2}}^{42} \frac{4}{x} - \frac{x}{8} d x = 12 ln (2) - \frac{63}{32}

= 12 ln (2) - \frac{63}{32} + \frac{63}{32} + \frac{63}{32} + 12 ln (2) - \frac{63}{32}

簡素化

= 24 ln (2)

グラフ

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