integral from 1 to 4 of (x/8-6/x)

解答

\int_{1}^{4} (\frac{x}{8} - \frac{6}{x}) d x

\frac{15}{16} - 12 ln (2)

十进制

- 7.38026 \dots

求解步骤

\int_{1}^{4} \frac{x}{8} - \frac{6}{x} d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{4} \frac{x}{8} d x - \int_{1}^{4} \frac{6}{x} d x

\int_{1}^{4} \frac{x}{8} d x = \frac{15}{16}

\int_{1}^{4} \frac{6}{x} d x = 12 ln (2)

= \frac{15}{16} - 12 ln (2)

\int_{2}^{5} 4 x^{2} d x

\int_{2}^{4} \frac{x}{x ^{2} - 1} d x

\int_{1}^{9} (15 - 3 x) d x

\int_{- 1}^{1} q q^{2} + 3 d q

\int_{0}^{\frac{π}{2}} - 6 sin (x) d x