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受欢迎的微积分 >

面积 x=4y^2,x+y=3

解答

面积

x = 4 y^{2}, x + y = 3

解答

\frac{343}{96}

+1

十进制

3.57291 \dots

求解步骤

对于

x = 4 y^{2}

将

y

移到一边:

y = \frac{x}{2}, y = - \frac{x}{2}

对于

x + y = 3

将

y

移到一边:

y = 3 - x

f_{1} (x) = \frac{x}{2}

f_{2} (x) = - \frac{x}{2}

要找到相交点，解

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

\frac{x}{2} = - \frac{x}{2} : x = 0

\frac{x}{2} = 3 - x : x = \frac{9}{4}

- \frac{x}{2} = 3 - x : x = 4

= \int_{0}^{\frac{9}{4}} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{\frac{9}{4}}^{4} ∣ f_{2} (x) - f_{3} (x) ∣ d x

= \int_{0}^{\frac{9}{4}} \frac{x}{2} - (- \frac{x}{2}) d x + \int_{\frac{9}{4}}^{4} - \frac{x}{2} - (3 - x) d x

\int_{0}^{\frac{9}{4}} \frac{x}{2} - (- \frac{x}{2}) d x = \frac{9}{4}

\int_{\frac{9}{4}}^{4} - \frac{x}{2} - (3 - x) d x = \frac{127}{96}

= \frac{9}{4} + \frac{127}{96}

化简

= \frac{343}{96}

作图

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