integral from 1 to 2 of (5-x)/(x^3)

解答

\int_{1}^{2} \frac{5 - x}{x ^{3}} d x

\frac{11}{8}

十进制

1.375

求解步骤

\int_{1}^{2} \frac{5 - x}{x ^{3}} d x

乘开

\frac{5 - x}{x ^{3}} : \frac{5}{x ^{3}} - \frac{1}{x ^{2}}

= \int_{1}^{2} \frac{5}{x ^{3}} - \frac{1}{x ^{2}} 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}^{2} \frac{5}{x ^{3}} d x - \int_{1}^{2} \frac{1}{x ^{2}} d x

\int_{1}^{2} \frac{5}{x ^{3}} d x = \frac{15}{8}

\int_{1}^{2} \frac{1}{x ^{2}} d x = \frac{1}{2}

= \frac{15}{8} - \frac{1}{2}

化简

\frac{15}{8} - \frac{1}{2} : \frac{11}{8}

= \frac{11}{8}

\frac{d}{d x} ((csc (x))^{2})

n = 1 \sum \infty e^{- 8 n}

t \to π lim (cos (\frac{2 t}{3}))

a re a f (x) = - x^{2} + 4, y + 2 x - 4 = 0

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