integral from 1 to 3 of (x-1)/(sqrt(x))

解

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

\frac{4}{3}

十進法表記

1.33333 \dots

解答ステップ

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

拡張

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

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

\int_{1}^{3} x d x = 23 - \frac{2}{3}

\int_{1}^{3} \frac{1}{x} d x = 23 - 2

= 23 - \frac{2}{3} - (23 - 2)

簡素化

23 - \frac{2}{3} - (23 - 2) : \frac{4}{3}

= \frac{4}{3}