aire 1/4 x^2,2x^2,3-x

Solution

aire

\frac{1}{4} x^{2}, 2 x^{2}, 3 - x

\frac{129}{8}

Notation décimale

16.125

étapes des solutions

Pour trouver les points d'intersection, résoudre

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

\frac{1}{4} x^{2} = 2 x^{2} : x = 0

\frac{1}{4} x^{2} = 3 - x : x = 2, x = - 6

2 x^{2} = 3 - x : x = 1, x = - \frac{3}{2}

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

= \int_{- 6}^{- \frac{3}{2}} \frac{1}{4} x^{2} - (3 - x) d x + \int_{- \frac{3}{2}}^{0} 2 x^{2} - \frac{1}{4} x^{2} d x + \int_{0}^{1} \frac{1}{4} x^{2} - 2 x^{2} d x + \int_{1}^{2} \frac{1}{4} x^{2} - (3 - x) d x

\int_{- 6}^{- \frac{3}{2}} \frac{1}{4} x^{2} - (3 - x) d x = \frac{405}{32}

\int_{- \frac{3}{2}}^{0} 2 x^{2} - \frac{1}{4} x^{2} d x = \frac{63}{32}

\int_{0}^{1} \frac{1}{4} x^{2} - 2 x^{2} d x = \frac{7}{12}

\int_{1}^{2} \frac{1}{4} x^{2} - (3 - x) d x = \frac{11}{12}

= \frac{405}{32} + \frac{63}{32} + \frac{7}{12} + \frac{11}{12}

Simplifier

= \frac{129}{8}

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