integral from-2 to 3 of (8z^3+3z-1)

解

\int_{- 2}^{3} (8 z^{3} + 3 z - 1) d z

\frac{265}{2}

十進法表記

132.5

解答ステップ

\int_{- 2}^{3} 8 z^{3} + 3 z - 1 d z

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_{- 2}^{3} 8 z^{3} d z + \int_{- 2}^{3} 3 z d z - \int_{- 2}^{3} 1 d z

\int_{- 2}^{3} 8 z^{3} d z = 130

\int_{- 2}^{3} 3 z d z = \frac{15}{2}

\int_{- 2}^{3} 1 d z = 5

= 130 + \frac{15}{2} - 5

簡素化

130 + \frac{15}{2} - 5 : \frac{265}{2}

= \frac{265}{2}