integral from-2 to 2 of (x+1)sqrt(4-x^2)

解

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

2 π

十進法表記

6.28318 \dots

解答ステップ

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

拡張

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

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

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

\int_{- 2}^{2} 4 - x^{2} d x = 2 π

= 0 + 2 π

簡素化

= 2 π