integral from 2 to 3 of (4+2x)^2

解

\int_{2}^{3} (4 + 2 x)^{2} d x

\frac{244}{3}

十進法表記

81.33333 \dots

解答ステップ

\int_{2}^{3} (4 + 2 x)^{2} d x

拡張

(4 + 2 x)^{2} : 16 + 16 x + 4 x^{2}

= \int_{2}^{3} 16 + 16 x + 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}^{3} 16 d x + \int_{2}^{3} 16 x d x + \int_{2}^{3} 4 x^{2} d x

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

\int_{2}^{3} 16 x d x = 40

\int_{2}^{3} 4 x^{2} d x = \frac{76}{3}

= 16 + 40 + \frac{76}{3}

簡素化

16 + 40 + \frac{76}{3} : \frac{244}{3}

= \frac{244}{3}