integral from 1 to 4 of (3/x-x^{-1/2})

解

\int_{1}^{4} (\frac{3}{x} - x^{- \frac{1}{2}}) d x

6 ln (2) - 2

十進法表記

2.15888 \dots

解答ステップ

\int_{1}^{4} \frac{3}{x} - x^{- \frac{1}{2}} d x

総和規則を適用する:

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

= \int_{1}^{4} \frac{3}{x} d x - \int_{1}^{4} x^{- \frac{1}{2}} d x

\int_{1}^{4} \frac{3}{x} d x = 6 ln (2)

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

= 6 ln (2) - 2