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受欢迎的微积分 >

面积 x=-y,x=2-y^2

解答

面积

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

解答

\frac{9}{2}

+1

十进制

4.5

求解步骤

对于

x = - y

将

y

移到一边:

y = - x

对于

x = 2 - y^{2}

将

y

移到一边:

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

f_{1} (x) = - x

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

要找到相交点，解

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

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

- x = - - x + 2 : x = 1

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

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

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

\int_{- 2}^{1} - x - - x + 2 d x = \frac{19}{6}

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

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

化简

= \frac{9}{2}

作图

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