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受欢迎的微积分 >

面积 x+y^2=42,x=y

解答

面积

x + y^{2} = 42, x = y

解答

\frac{2197}{6}

+1

十进制

366.16666 \dots

求解步骤

对于

x + y^{2} = 42

将

y

移到一边:

y = 42 - x, y = - 42 - x

对于

x = y

将

y

移到一边:

y = x

f_{1} (x) = 42 - x

f_{2} (x) = - 42 - x

要找到相交点，解

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

42 - x = - 42 - x : x = 42

42 - x = x : x = 6

- 42 - x = x : x = - 7

= \int_{- 7}^{6} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{6}^{42} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{- 7}^{6} - 42 - x - x d x + \int_{6}^{42} 42 - x - (- 42 - x) d x

\int_{- 7}^{6} - 42 - x - x d x = \frac{469}{6}

\int_{6}^{42} 42 - x - (- 42 - x) d x = 288

= \frac{469}{6} + 288

化简

= \frac{2197}{6}

作图

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