integral from 1 to 6 of t^2-2t-15

解

\int_{1}^{6} t^{2} - 2 t - 15 d t

- \frac{115}{3}

十進法表記

- 38.33333 \dots

解答ステップ

\int_{1}^{6} t^{2} - 2 t - 15 d t

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}^{6} t^{2} d t - \int_{1}^{6} 2 t d t - \int_{1}^{6} 15 d t

\int_{1}^{6} t^{2} d t = \frac{215}{3}

\int_{1}^{6} 2 t d t = 35

\int_{1}^{6} 15 d t = 75

= \frac{215}{3} - 35 - 75

簡素化

\frac{215}{3} - 35 - 75 : - \frac{115}{3}

= - \frac{115}{3}