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受欢迎的微积分 >

面积 y=x-2,x=y^2

解答

面积

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

解答

\frac{9}{2}

+1

十进制

4.5

求解步骤

对于

x = y^{2}

将

y

移到一边:

y = x, y = - x

f_{1} (x) = x - 2

f_{2} (x) = x

要找到相交点，解

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

x - 2 = x : x = 4

x - 2 = - x : x = 1

x = - x : x = 0

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

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

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

\int_{1}^{4} x - 2 - x d x = \frac{19}{6}

= \frac{4}{3} + \frac{19}{6}

化简

= \frac{9}{2}

作图

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