面积 (1/(14x^2)),x,(x/4)

解答

面积

(\frac{1}{14 x ^{2}}), x, (\frac{x}{4})

\frac{6 3 14 - 3 \cdot 2 ^{\frac{2}{3}} 3 7}{56}

十进制

0.09555 \dots

求解步骤

要找到相交点，解

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

(\frac{1}{14 x ^{2}}) = x : x = \frac{1}{3 14}

(\frac{1}{14 x ^{2}}) = (\frac{x}{4}) : x = 3 \frac{2}{7}

x = (\frac{x}{4}) : x = 0

= \int_{0}^{\frac{1}{3 14}} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{\frac{1}{3 14}}^{3 \frac{2}{7}} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{0}^{\frac{1}{3 14}} x - (\frac{x}{4}) d x + \int_{\frac{1}{3 14}}^{3 \frac{2}{7}} (\frac{1}{14 x ^{2}}) - (\frac{x}{4}) d x

\int_{0}^{\frac{1}{3 14}} x - (\frac{x}{4}) d x = \frac{3}{8 \cdot 1 4 ^{\frac{2}{3}}}

\int_{\frac{1}{3 14}}^{3 \frac{2}{7}} (\frac{1}{14 x ^{2}}) - (\frac{x}{4}) d x = \frac{- 4 3 49 \cdot 2 ^{\frac{2}{3}} + 9 3 2 \cdot 7 ^{\frac{2}{3}} - 2 \cdot 1 4 ^{\frac{2}{3}}}{56 3 14 \cdot 2 ^{\frac{2}{3}}}

= \frac{3}{8 \cdot 1 4 ^{\frac{2}{3}}} + \frac{- 4 3 49 \cdot 2 ^{\frac{2}{3}} + 9 3 2 \cdot 7 ^{\frac{2}{3}} - 2 \cdot 1 4 ^{\frac{2}{3}}}{56 3 14 \cdot 2 ^{\frac{2}{3}}}

化简

= \frac{6 3 14 - 3 \cdot 2 ^{\frac{2}{3}} 3 7}{56}

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