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面积 y^2-6x=1,x-y=1

解答

面积

y^{2} - 6 x = 1, x - y = 1

解答

\frac{128}{9}

+1

十进制

14.22222 \dots

求解步骤

对于

y^{2} - 6 x = 1

将

y

移到一边:

y = 1 + 6 x, y = - 1 + 6 x

对于

x - y = 1

将

y

移到一边:

y = - 1 + x

f_{1} (x) = 1 + 6 x

f_{2} (x) = - 1 + 6 x

要找到相交点，解

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

1 + 6 x = - 1 + 6 x : x = - \frac{1}{6}

1 + 6 x = - 1 + x : x = 8

- 1 + 6 x = - 1 + x : x = 0

= \int_{- \frac{1}{6}}^{0} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{0}^{8} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- \frac{1}{6}}^{0} 1 + 6 x - (- 1 + 6 x) d x + \int_{0}^{8} 1 + 6 x - (- 1 + x) d x

\int_{- \frac{1}{6}}^{0} 1 + 6 x - (- 1 + 6 x) d x = \frac{2}{9}

\int_{0}^{8} 1 + 6 x - (- 1 + x) d x = 14

= \frac{2}{9} + 14

化简

= \frac{128}{9}

作图

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