integral from 0 to t of x^2-3x+2

解

\int_{0}^{t} x^{2} - 3 x + 2 d x

2 t + \frac{t ^{3}}{3} - \frac{3 t ^{2}}{2}

解答ステップ

\int_{0}^{t} x^{2} - 3 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}^{t} 2 d x + \int_{0}^{t} x^{2} d x - \int_{0}^{t} 3 x d x

\int_{0}^{t} 2 d x = 2 t

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

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

= 2 t + \frac{t ^{3}}{3} - \frac{3 t ^{2}}{2}