面积 7x, 1/x ,x

解答

面积

7 x, \frac{1}{x}, x

ln (7)

十进制

1.94591 \dots

求解步骤

要找到相交点，解

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

7 x = \frac{1}{x} : x = \frac{1}{7}, x = - \frac{1}{7}

7 x = x : x = 0

\frac{1}{x} = x : x = 1, x = - 1

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

= \int_{- 1}^{- \frac{1}{7}} \frac{1}{x} - x d x + \int_{- \frac{1}{7}}^{0} ∣ 7 x - x ∣ d x + \int_{0}^{\frac{1}{7}} ∣ 7 x - x ∣ d x + \int_{\frac{1}{7}}^{1} x - \frac{1}{x} d x

\int_{- 1}^{- \frac{1}{7}} \frac{1}{x} - x d x = \frac{1}{2} ln (7) - \frac{3}{7}

\int_{- \frac{1}{7}}^{0} ∣ 7 x - x ∣ d x = \frac{3}{7}

\int_{0}^{\frac{1}{7}} ∣ 7 x - x ∣ d x = \frac{3}{7}

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

= \frac{1}{2} ln (7) - \frac{3}{7} + \frac{3}{7} + \frac{3}{7} - \frac{3}{7} + \frac{1}{2} ln (7)

化简

= ln (7)

t an g e n t f (x) = x^{4} - 25 x^{2} + 144, at x = - 2

\frac{d}{d x} (sech (ln (x^{2})))

\int_{0}^{1} arctan (5 x + 3) d x

t an g e n t f (x) = \frac{2 x}{x + 2}, (2, 1)

in v erse l a pl a ce \frac{1}{( ( s + 1 ) ^{2} + 4 )}