面积 y=9x,y= 3/7 x,y=52-x^2

解答

面积

y = 9 x, y = \frac{3}{7} x, y = 52 - x^{2}

\frac{194550}{343}

十进制

567.20116 \dots

求解步骤

要找到相交点，解

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

9 x = \frac{3}{7} x : x = 0

9 x = 52 - x^{2} : x = - 13, x = 4

\frac{3}{7} x = 52 - x^{2} : x = - \frac{52}{7}, x = 7

= \int_{- 13}^{- \frac{52}{7}} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{- \frac{52}{7}}^{0} ∣ f_{2} (x) - f_{1} (x) ∣ d x + \int_{0}^{4} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{4}^{7} ∣ f_{2} (x) - f_{3} (x) ∣ d x

= \int_{- 13}^{- \frac{52}{7}} 9 x - (52 - x^{2}) d x + \int_{- \frac{52}{7}}^{0} \frac{3}{7} x - 9 x d x + \int_{0}^{4} 9 x - \frac{3}{7} x d x + \int_{4}^{7} \frac{3}{7} x - (52 - x^{2}) d x

\int_{- 13}^{- \frac{52}{7}} 9 x - (52 - x^{2}) d x = \frac{141453}{686}

\int_{- \frac{52}{7}}^{0} \frac{3}{7} x - 9 x d x = \frac{81120}{343}

\int_{0}^{4} 9 x - \frac{3}{7} x d x = \frac{480}{7}

\int_{4}^{7} \frac{3}{7} x - (52 - x^{2}) d x = \frac{783}{14}

= \frac{141453}{686} + \frac{81120}{343} + \frac{480}{7} + \frac{783}{14}

化简

= \frac{194550}{343}

f (x) = \frac{x}{x ^{2} + 25}

\int 2 x (x^{2} + 3)^{9} d x

\int_{0}^{6} x^{3} e^{x} d x

n = 1 \sum \infty \frac{1}{n ^{2} - 1}

\int_{0}^{1} x^{4} e^{6 x} d x