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面积 x+y^2=56,x+y=0

解答

面积

x + y^{2} = 56, x + y = 0

解答

\frac{1125}{2}

+1

十进制

562.5

求解步骤

对于

x + y^{2} = 56

将

y

移到一边:

y = 56 - x, y = - 56 - x

对于

x + y = 0

将

y

移到一边:

y = - x

f_{1} (x) = 56 - x

f_{2} (x) = - 56 - x

要找到相交点，解

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

56 - x = - 56 - x : x = 56

56 - x = - x : x = - 8

- 56 - x = - x : x = 7

= \int_{- 8}^{7} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{7}^{56} ∣ f_{2} (x) - f_{1} (x) ∣ d x

= \int_{- 8}^{7} 56 - x - (- x) d x + \int_{7}^{56} - 56 - x - 56 - x d x

\int_{- 8}^{7} 56 - x - (- x) d x = \frac{631}{6}

\int_{7}^{56} - 56 - x - 56 - x d x = \frac{1372}{3}

= \frac{631}{6} + \frac{1372}{3}

化简

= \frac{1125}{2}

作图

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