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受欢迎的微积分 >

面积 y=x,4x+y^2=12

解答

面积

y = x, 4 x + y^{2} = 12

解答

\frac{64}{3}

+1

十进制

21.33333 \dots

求解步骤

对于

4 x + y^{2} = 12

将

y

移到一边:

y = 2 3 - x, y = - 2 3 - x

f_{1} (x) = x

f_{2} (x) = 2 3 - x

要找到相交点，解

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

x = 2 3 - x : x = 2

x = - 2 3 - x : x = - 6

2 3 - x = - 2 3 - x : x = 3

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

= \int_{- 6}^{2} x - (- 2 3 - x) d x + \int_{2}^{3} - 2 3 - x - 2 3 - x d x

\int_{- 6}^{2} x - (- 2 3 - x) d x = \frac{56}{3}

\int_{2}^{3} - 2 3 - x - 2 3 - x d x = \frac{8}{3}

= \frac{56}{3} + \frac{8}{3}

化简

= \frac{64}{3}

作图

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