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人気のある微分積分 >

面積 y=5x^2,y^2= 1/5 x

解

面積

y = 5 x^{2}, y^{2} = \frac{1}{5} x

解

\frac{1}{75}

+1

十進法表記

0.01333 \dots

解答ステップ

以下のために

y

を分離:

y^{2} = \frac{1}{5} x : y = \frac{x}{5}, y = - \frac{x}{5}

f_{1} (x) = 5 x^{2}

f_{2} (x) = \frac{x}{5}

交点を見つけるには以下を解く:

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

5 x^{2} = \frac{x}{5} : x = 0, x = \frac{1}{5}

5 x^{2} = - \frac{x}{5} : x = 0

\frac{x}{5} = - \frac{x}{5} : x = 0

= \int_{0}^{\frac{1}{5}} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{0}^{\frac{1}{5}} 5 x^{2} - \frac{x}{5} d x

\int_{0}^{\frac{1}{5}} 5 x^{2} - \frac{x}{5} d x = \frac{1}{75}

= \frac{1}{75}

グラフ

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