面積 y=x,y=4x,y=-x+2

解

面積

y = x, y = 4 x, y = - x + 2

\frac{3}{5}

十進法表記

0.6

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 = 4 x : x = 0

x = - x + 2 : x = 1

4 x = - x + 2 : x = \frac{2}{5}

= \int_{0}^{\frac{2}{5}} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{\frac{2}{5}}^{1} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{0}^{\frac{2}{5}} ∣ x - 4 x ∣ d x + \int_{\frac{2}{5}}^{1} ∣ x - (- x + 2) ∣ d x

\int_{0}^{\frac{2}{5}} ∣ x - 4 x ∣ d x = \frac{6}{25}

\int_{\frac{2}{5}}^{1} ∣ x - (- x + 2) ∣ d x = \frac{9}{25}

= \frac{6}{25} + \frac{9}{25}

簡素化

= \frac{3}{5}