面積 y=8x,y=0,y=x^2-9

解

面積

y = 8 x, y = 0, y = x^{2} - 9

\frac{472}{3}

十進法表記

157.33333 \dots

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)

8 x = 0 : x = 0

8 x = x^{2} - 9 : x = 9, x = - 1

0 = x^{2} - 9 : x = 3, x = - 3

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

= \int_{- 3}^{- 1} 0 - (x^{2} - 9) d x + \int_{- 1}^{0} ∣ 8 x - 0 ∣ d x + \int_{0}^{3} ∣ 8 x - 0 ∣ d x + \int_{3}^{9} 8 x - (x^{2} - 9) d x

\int_{- 3}^{- 1} 0 - (x^{2} - 9) d x = \frac{28}{3}

\int_{- 1}^{0} ∣ 8 x - 0 ∣ d x = 4

\int_{0}^{3} ∣ 8 x - 0 ∣ d x = 36

\int_{3}^{9} 8 x - (x^{2} - 9) d x = 108

= \frac{28}{3} + 4 + 36 + 108

簡素化

= \frac{472}{3}