integral from 0 to 1 of x^2+3x

解

\int_{0}^{1} x^{2} + 3 x d x

\frac{11}{6}

十進法表記

1.83333 \dots

解答ステップ

\int_{0}^{1} x^{2} + 3 x 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_{0}^{1} x^{2} d x + \int_{0}^{1} 3 x d x

\int_{0}^{1} x^{2} d x = \frac{1}{3}

\int_{0}^{1} 3 x d x = \frac{3}{2}

= \frac{1}{3} + \frac{3}{2}

簡素化

\frac{1}{3} + \frac{3}{2} : \frac{11}{6}

= \frac{11}{6}