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人気のある微分積分 >

面積 7x, 1/x ,x

解

面積

7 x, \frac{1}{x}, x

解

ln (7)

+1

十進法表記

1.94591 \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)

7 x = \frac{1}{x} : x = \frac{1}{7}, x = - \frac{1}{7}

7 x = x : x = 0

\frac{1}{x} = x : x = 1, x = - 1

= \int_{- 1}^{- \frac{1}{7}} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{- \frac{1}{7}}^{0} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{0}^{\frac{1}{7}} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{\frac{1}{7}}^{1} ∣ f_{3} (x) - f_{2} (x) ∣ d x

= \int_{- 1}^{- \frac{1}{7}} \frac{1}{x} - x d x + \int_{- \frac{1}{7}}^{0} ∣ 7 x - x ∣ d x + \int_{0}^{\frac{1}{7}} ∣ 7 x - x ∣ d x + \int_{\frac{1}{7}}^{1} x - \frac{1}{x} d x

\int_{- 1}^{- \frac{1}{7}} \frac{1}{x} - x d x = \frac{1}{2} ln (7) - \frac{3}{7}

\int_{- \frac{1}{7}}^{0} ∣ 7 x - x ∣ d x = \frac{3}{7}

\int_{0}^{\frac{1}{7}} ∣ 7 x - x ∣ d x = \frac{3}{7}

\int_{\frac{1}{7}}^{1} x - \frac{1}{x} d x = - \frac{3}{7} + \frac{1}{2} ln (7)

= \frac{1}{2} ln (7) - \frac{3}{7} + \frac{3}{7} + \frac{3}{7} - \frac{3}{7} + \frac{1}{2} ln (7)

簡素化

= ln (7)

グラフ

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