integral from-2 to 3 of 8x^3+4x^2-7

解

\int_{- 2}^{3} 8 x^{3} + 4 x^{2} - 7 d x

\frac{425}{3}

十進法表記

141.66666 \dots

解答ステップ

\int_{- 2}^{3} 8 x^{3} + 4 x^{2} - 7 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_{- 2}^{3} 8 x^{3} d x + \int_{- 2}^{3} 4 x^{2} d x - \int_{- 2}^{3} 7 d x

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

\int_{- 2}^{3} 4 x^{2} d x = \frac{140}{3}

\int_{- 2}^{3} 7 d x = 35

= 130 + \frac{140}{3} - 35

簡素化

130 + \frac{140}{3} - 35 : \frac{425}{3}

= \frac{425}{3}