面积 y=x+1,y=7x-17,y=-2x-2

解答

面积

y = x + 1, y = 7 x - 17, y = - 2 x - 2

16

求解步骤

要找到相交点，解

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

x + 1 = 7 x - 17 : x = 3

x + 1 = - 2 x - 2 : x = - 1

7 x - 17 = - 2 x - 2 : x = \frac{5}{3}

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

= \int_{- 1}^{\frac{5}{3}} ∣ x + 1 - (- 2 x - 2) ∣ d x + \int_{\frac{5}{3}}^{3} ∣ 7 x - 17 - (x + 1) ∣ d x

\int_{- 1}^{\frac{5}{3}} ∣ x + 1 - (- 2 x - 2) ∣ d x = \frac{32}{3}

\int_{\frac{5}{3}}^{3} ∣ 7 x - 17 - (x + 1) ∣ d x = \frac{16}{3}

= \frac{32}{3} + \frac{16}{3}

化简

= 16

a re a y = ∣ 9 x ∣, y = x^{2} - 10

\int \frac{2 x + 1}{x ^{2} + 4} d x

y^{^{''}} + 12 y^{^{'}} + 24 y = 4381 e^{2 t} cos (13 t)

\int e^{x} sec (e^{x}) d x

\int tan^{5} (7 x) d x