integral from 0 to 1 of (e^x+3x-5x^2)

解

\int_{0}^{1} (e^{x} + 3 x - 5 x^{2}) d x

e - \frac{7}{6}

十進法表記

1.55161 \dots

解答ステップ

\int_{0}^{1} e^{x} + 3 x - 5 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_{0}^{1} e^{x} d x + \int_{0}^{1} 3 x d x - \int_{0}^{1} 5 x^{2} d x

\int_{0}^{1} e^{x} d x = e - 1

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

\int_{0}^{1} 5 x^{2} d x = \frac{5}{3}

= e - 1 + \frac{3}{2} - \frac{5}{3}

分数を組み合わせる

- 1 + \frac{3}{2} - \frac{5}{3} : - \frac{7}{6}

= e - \frac{7}{6}