面積 y=sqrt(x),y=2x-15,y=0

解

面積

y = x, y = 2 x - 15, y = 0

\frac{63}{4}

十進法表記

15.75

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 = 2 x - 15 : x = 9

x = 0 : x = 0

2 x - 15 = 0 : x = \frac{15}{2}

= \int_{0}^{\frac{15}{2}} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{\frac{15}{2}}^{9} ∣ f_{2} (x) - f_{1} (x) ∣ d x

= \int_{0}^{\frac{15}{2}} x - 0 d x + \int_{\frac{15}{2}}^{9} 2 x - 15 - x d x

\int_{0}^{\frac{15}{2}} x - 0 d x = \frac{5 15}{2}

\int_{\frac{15}{2}}^{9} 2 x - 15 - x d x = \frac{63}{4} - \frac{5 15}{2}

= \frac{5 15}{2} + \frac{63}{4} - \frac{5 15}{2}

簡素化

= \frac{63}{4}