面積 2x,5, 2/(x^2)

解

面積

2 x, 5, \frac{2}{x ^{2}}

は発散する - 210 + \frac{37}{4}

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)

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

2 x = 5 : x = \frac{5}{2}

\frac{2}{x ^{2}} = 5 : x = \frac{2}{5}, x = - \frac{2}{5}

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

= \int_{- \frac{2}{5}}^{\frac{2}{5}} \frac{2}{x ^{2}} - 5 d x + \int_{\frac{2}{5}}^{1} \frac{2}{x ^{2}} - 5 d x + \int_{1}^{\frac{5}{2}} ∣ 2 x - 5 ∣ d x

\int_{- \frac{2}{5}}^{\frac{2}{5}} \frac{2}{x ^{2}} - 5 d x =

は発散する

\int_{\frac{2}{5}}^{1} \frac{2}{x ^{2}} - 5 d x = 7 - 210

\int_{1}^{\frac{5}{2}} ∣ 2 x - 5 ∣ d x = \frac{9}{4}

= は発散する + 7 - 210 + \frac{9}{4}

簡素化

= は発散する - 210 + \frac{37}{4}