integral from-2 to 2 of (x+3)^2

解

\int_{- 2}^{2} (x + 3)^{2} d x

\frac{124}{3}

十進法表記

41.33333 \dots

解答ステップ

\int_{- 2}^{2} (x + 3)^{2} d x

拡張

(x + 3)^{2} : x^{2} + 6 x + 9

= \int_{- 2}^{2} x^{2} + 6 x + 9 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} 6 x d x + \int_{- 2}^{2} 9 d x

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

\int_{- 2}^{2} 6 x d x = 0

\int_{- 2}^{2} 9 d x = 36

= \frac{16}{3} + 0 + 36

簡素化

\frac{16}{3} + 0 + 36 : \frac{124}{3}

= \frac{124}{3}