面積 y=x,y=3x,y=-x+4

解

面積

y = x, y = 3 x, y = - x + 4

2

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 = - x + 4 : x = 2

3 x = - x + 4 : x = 1

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

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

\int_{0}^{1} ∣ x - 3 x ∣ d x = 1

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

= 1 + 1

簡素化

= 2