integral from-2 to 2 of (2x-1)^2

解

\int_{- 2}^{2} (2 x - 1)^{2} d x

\frac{76}{3}

十進法表記

25.33333 \dots

解答ステップ

\int_{- 2}^{2} (2 x - 1)^{2} d x

拡張

(2 x - 1)^{2} : 4 x^{2} - 4 x + 1

= \int_{- 2}^{2} 4 x^{2} - 4 x + 1 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} 4 x^{2} d x - \int_{- 2}^{2} 4 x d x + \int_{- 2}^{2} 1 d x

\int_{- 2}^{2} 4 x^{2} d x = \frac{64}{3}

\int_{- 2}^{2} 4 x d x = 0

\int_{- 2}^{2} 1 d x = 4

= \frac{64}{3} - 0 + 4

簡素化

\frac{64}{3} - 0 + 4 : \frac{76}{3}

= \frac{76}{3}