integral from-2 to 2 of (x+17)^2

解

\int_{- 2}^{2} (x + 17)^{2} d x

\frac{3484}{3}

十進法表記

1161.33333 \dots

解答ステップ

\int_{- 2}^{2} (x + 17)^{2} d x

拡張

(x + 17)^{2} : x^{2} + 34 x + 289

= \int_{- 2}^{2} x^{2} + 34 x + 289 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}^{2} x^{2} d x + \int_{- 2}^{2} 34 x d x + \int_{- 2}^{2} 289 d x

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

\int_{- 2}^{2} 34 x d x = 0

\int_{- 2}^{2} 289 d x = 1156

= \frac{16}{3} + 0 + 1156

簡素化

\frac{16}{3} + 0 + 1156 : \frac{3484}{3}

= \frac{3484}{3}