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面积 x=4-(y-2)^2,y=x

解答

面积

x = 4 - (y - 2)^{2}, y = x

解答

\frac{9}{2}

+1

十进制

4.5

求解步骤

对于

x = 4 - (y - 2)^{2}

将

y

移到一边:

y = - x + 4 + 2, y = - - x + 4 + 2

f_{1} (x) = - x + 4 + 2

f_{2} (x) = - - x + 4 + 2

要找到相交点，解

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

- x + 4 + 2 = - - x + 4 + 2 : x = 4

- x + 4 + 2 = x : x = 3

- - x + 4 + 2 = x : x = 0

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

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

\int_{0}^{3} - - x + 4 + 2 - x d x = \frac{19}{6}

\int_{3}^{4} - x + 4 + 2 - (- - x + 4 + 2) d x = \frac{4}{3}

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

化简

= \frac{9}{2}

作图

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