integral from 1 to 3 of (x^2+2x+1)

解

\int_{1}^{3} (x^{2} + 2 x + 1) d x

\frac{56}{3}

十進法表記

18.66666 \dots

解答ステップ

\int_{1}^{3} x^{2} + 2 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_{1}^{3} x^{2} d x + \int_{1}^{3} 2 x d x + \int_{1}^{3} 1 d x

\int_{1}^{3} x^{2} d x = \frac{26}{3}

\int_{1}^{3} 2 x d x = 8

\int_{1}^{3} 1 d x = 2

= \frac{26}{3} + 8 + 2

簡素化

\frac{26}{3} + 8 + 2 : \frac{56}{3}

= \frac{56}{3}