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面积 y=3sqrt(x),x+y=4,y=1

解答

面积

y = 3 x, x + y = 4, y = 1

解答

\frac{82}{27}

+1

十进制

3.03703 \dots

求解步骤

对于

x + y = 4

将

y

移到一边:

y = 4 - x

f_{1} (x) = 3 x

f_{2} (x) = 4 - x

要找到相交点，解

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

3 x = 4 - x : x = 1

3 x = 1 : x = \frac{1}{9}

4 - x = 1 : x = 3

= \int_{\frac{1}{9}}^{1} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{1}^{3} ∣ f_{3} (x) - f_{2} (x) ∣ d x

= \int_{\frac{1}{9}}^{1} 3 x - 1 d x + \int_{1}^{3} ∣ 1 - (4 - x) ∣ d x

\int_{\frac{1}{9}}^{1} 3 x - 1 d x = \frac{28}{27}

\int_{1}^{3} ∣ 1 - (4 - x) ∣ d x = 2

= \frac{28}{27} + 2

化简

= \frac{82}{27}

作图

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