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受欢迎的微积分 >

面积 x+y^2=12,x+y=0

解答

面积

x + y^{2} = 12, x + y = 0

解答

\frac{343}{6}

+1

十进制

57.16666 \dots

求解步骤

对于

x + y^{2} = 12

将

y

移到一边:

y = 12 - x, y = - 12 - x

对于

x + y = 0

将

y

移到一边:

y = - x

f_{1} (x) = 12 - x

f_{2} (x) = - 12 - x

要找到相交点，解

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

12 - x = - 12 - x : x = 12

12 - x = - x : x = - 4

- 12 - x = - x : x = 3

= \int_{- 4}^{3} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{3}^{12} ∣ f_{2} (x) - f_{1} (x) ∣ d x

= \int_{- 4}^{3} 12 - x - (- x) d x + \int_{3}^{12} - 12 - x - 12 - x d x

\int_{- 4}^{3} 12 - x - (- x) d x = \frac{127}{6}

\int_{3}^{12} - 12 - x - 12 - x d x = 36

= \frac{127}{6} + 36

化简

= \frac{343}{6}

作图

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