面积 y=1.25x,x=8.5-y^2

解答

面积

y = 1.25 x, x = 8.5 - y^{2}

33.97938 \dots

求解步骤

对于

x = 8.5 - y^{2}

将

y

移到一边:

y = - x + 8.5, y = - - x + 8.5

f_{1} (x) = 1.25 x

f_{2} (x) = - x + 8.5

要找到相交点，解

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

1.25 x = - x + 8.5 : x = \frac{- 1 + 54.125}{3.125}

1.25 x = - - x + 8.5 : x = \frac{- 1 - 54.125}{3.125}

- x + 8.5 = - - x + 8.5 : x = 8.5

= \int_{\frac{- 1 - 54.125}{3.125}}^{\frac{- 1 + 54.125}{3.125}} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{\frac{- 1 + 54.125}{3.125}}^{8.5} ∣ f_{3} (x) - f_{2} (x) ∣ d x

= \int_{\frac{- 1 - 54.125}{3.125}}^{\frac{- 1 + 54.125}{3.125}} 1.25 x - (- - x + 8.5) d x + \int_{\frac{- 1 + 54.125}{3.125}}^{8.5} - - x + 8.5 - - x + 8.5 d x

\int_{\frac{- 1 - 54.125}{3.125}}^{\frac{- 1 + 54.125}{3.125}} 1.25 x - (- - x + 8.5) d x = 12.05794 \dots

\int_{\frac{- 1 + 54.125}{3.125}}^{8.5} - - x + 8.5 - - x + 8.5 d x = 21.92144 \dots

= 12.05794 \dots + 21.92144 \dots

化简

= 33.97938 \dots

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