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人気のある微分積分 >

面積 y=x-2,x=y^2

解

面積

y = x - 2, x = y^{2}

解

\frac{9}{2}

+1

十進法表記

4.5

解答ステップ

以下のために

y

を分離:

x = y^{2} : y = x, y = - x

f_{1} (x) = x - 2

f_{2} (x) = x

交点を見つけるには以下を解く:

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

x - 2 = x : x = 4

x - 2 = - x : x = 1

x = - x : x = 0

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

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

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

\int_{1}^{4} x - 2 - x d x = \frac{19}{6}

= \frac{4}{3} + \frac{19}{6}

簡素化

= \frac{9}{2}

グラフ

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