面积 y=28-x^2,y=0.6x,y=3x

解答

面积

y = 28 - x^{2}, y = 0.6 x, y = 3 x

\frac{7399}{750} + 61.79866 \dots

十进制

71.664

求解步骤

要找到相交点，解

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

28 - x^{2} = 0.6 x : x = - \frac{28}{5}, x = 5

28 - x^{2} = 3 x : x = - 7, x = 4

0.6 x = 3 x : x = 0

= \int_{- 7}^{- \frac{28}{5}} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{- \frac{28}{5}}^{0} ∣ f_{3} (x) - f_{2} (x) ∣ d x + \int_{0}^{4} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{4}^{5} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{- 7}^{- \frac{28}{5}} 28 - x^{2} - 3 x d x + \int_{- \frac{28}{5}}^{0} ∣ 3 x - 0.6 x ∣ d x + \int_{0}^{4} ∣ 0.6 x - 3 x ∣ d x + \int_{4}^{5} 28 - x^{2} - 0.6 x d x

\int_{- 7}^{- \frac{28}{5}} 28 - x^{2} - 3 x d x = \frac{7399}{750}

\int_{- \frac{28}{5}}^{0} ∣ 3 x - 0.6 x ∣ d x = 37.632

\int_{0}^{4} ∣ 0.6 x - 3 x ∣ d x = 19.2

\int_{4}^{5} 28 - x^{2} - 0.6 x d x = 4.96666 \dots

= \frac{7399}{750} + 37.632 + 19.2 + 4.96666 \dots

化简

= \frac{7399}{750} + 61.79866 \dots

\int \frac{3}{sec ( x ) - 1} d x

x \to a lim (2 f (x))

\frac{d}{d x} (cos (x + 1))

t^{2} \frac{d y}{d t} = - y

\frac{d}{d x} (6 x y + 5 x^{2})