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受欢迎的微积分 >

面积 x=y,x=y^2

解答

面积

x = y, x = y^{2}

解答

\frac{1}{6}

+1

十进制

0.16666 \dots

求解步骤

对于

x = y

将

y

移到一边:

y = x

对于

x = y^{2}

将

y

移到一边:

y = x, y = - x

f_{1} (x) = x

f_{2} (x) = x

要找到相交点，解

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

x = x : x = 1, x = 0

x = - x : x = 0

x = - x : x = 0

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

= \int_{0}^{1} x - x d x

\int_{0}^{1} x - x d x = \frac{1}{6}

= \frac{1}{6}

作图

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