integral from 1/2 to 1 of (x^{-3}-16)

解

\int_{\frac{1}{2}}^{1} (x^{- 3} - 16) d x

- \frac{13}{2}

十進法表記

- 6.5

解答ステップ

\int_{\frac{1}{2}}^{1} x^{- 3} - 16 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_{\frac{1}{2}}^{1} x^{- 3} d x - \int_{\frac{1}{2}}^{1} 16 d x

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

\int_{\frac{1}{2}}^{1} 16 d x = 8

= \frac{3}{2} - 8

簡素化

\frac{3}{2} - 8 : - \frac{13}{2}

= - \frac{13}{2}