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

解

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

\frac{1}{6}

十進法表記

0.16666 \dots

解答ステップ

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

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

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

\int_{1}^{\frac{3}{2}} \frac{1}{3} x d x = \frac{5}{24}

= 1 - \frac{5}{8} - \frac{5}{24}

簡素化

1 - \frac{5}{8} - \frac{5}{24} : \frac{1}{6}

= \frac{1}{6}