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受欢迎的微积分 >

面积 y=x-3,y^2=2x+18

解答

面积

y = x - 3, y^{2} = 2 x + 18

解答

\frac{250}{3}

+1

十进制

83.33333 \dots

求解步骤

对于

y^{2} = 2 x + 18

将

y

移到一边:

y = 2 x + 18, y = - 2 x + 18

f_{1} (x) = x - 3

f_{2} (x) = 2 x + 18

要找到相交点，解

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

x - 3 = 2 x + 18 : x = 9

x - 3 = - 2 x + 18 : x = - 1

2 x + 18 = - 2 x + 18 : x = - 9

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

= \int_{- 9}^{- 1} 2 x + 18 - (- 2 x + 18) d x + \int_{- 1}^{9} x - 3 - 2 x + 18 d x

\int_{- 9}^{- 1} 2 x + 18 - (- 2 x + 18) d x = \frac{128}{3}

\int_{- 1}^{9} x - 3 - 2 x + 18 d x = \frac{122}{3}

= \frac{128}{3} + \frac{122}{3}

化简

= \frac{250}{3}

作图

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