面积 0,5x,x^2-6

解答

面积

0, 5 x, x^{2} - 6

\frac{305}{6}

十进制

50.83333 \dots

求解步骤

要找到相交点，解

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

5 x = x^{2} - 6 : x = 6, x = - 1

5 x = 0 : x = 0

x^{2} - 6 = 0 : x = 6, x = - 6

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

= \int_{- 6}^{- 1} x^{2} - 6 - 0 d x + \int_{- 1}^{0} ∣ 5 x - 0 ∣ d x + \int_{0}^{6} ∣ 5 x - 0 ∣ d x + \int_{6}^{6} x^{2} - 6 - 5 x d x

\int_{- 6}^{- 1} x^{2} - 6 - 0 d x = 46 - \frac{17}{3}

\int_{- 1}^{0} ∣ 5 x - 0 ∣ d x = \frac{5}{2}

\int_{0}^{6} ∣ 5 x - 0 ∣ d x = 15

\int_{6}^{6} x^{2} - 6 - 5 x d x = 39 - 46

= 46 - \frac{17}{3} + \frac{5}{2} + 15 + 39 - 46

化简

= \frac{305}{6}

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