integral from 3 to 6 of x^3+x-2

解

\int_{3}^{6} x^{3} + x - 2 d x

\frac{1245}{4}

十進法表記

311.25

解答ステップ

\int_{3}^{6} x^{3} + x - 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_{3}^{6} x^{3} d x + \int_{3}^{6} x d x - \int_{3}^{6} 2 d x

\int_{3}^{6} x^{3} d x = \frac{1215}{4}

\int_{3}^{6} x d x = \frac{27}{2}

\int_{3}^{6} 2 d x = 6

= \frac{1215}{4} + \frac{27}{2} - 6

簡素化

\frac{1215}{4} + \frac{27}{2} - 6 : \frac{1245}{4}

= \frac{1245}{4}