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人気のある微分積分 >

面積 x^3,-x,1

解

面積

x^{3}, - x, 1

解

\frac{5}{4}

+1

十進法表記

1.25

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)

x^{3} = - x : x = 0

x^{3} = 1 : x = 1

- x = 1 : x = - 1

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

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

\int_{- 1}^{0} ∣ - x - 1 ∣ d x = \frac{1}{2}

\int_{0}^{1} x^{3} - 1 d x = \frac{3}{4}

= \frac{1}{2} + \frac{3}{4}

簡素化

= \frac{5}{4}

グラフ

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