integral from 2 to 4 of x^2+2x-3

解

\int_{2}^{4} x^{2} + 2 x - 3 d x

\frac{74}{3}

十進法表記

24.66666 \dots

解答ステップ

\int_{2}^{4} x^{2} + 2 x - 3 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}^{4} x^{2} d x + \int_{2}^{4} 2 x d x - \int_{2}^{4} 3 d x

\int_{2}^{4} x^{2} d x = \frac{56}{3}

\int_{2}^{4} 2 x d x = 12

\int_{2}^{4} 3 d x = 6

= \frac{56}{3} + 12 - 6

簡素化

\frac{56}{3} + 12 - 6 : \frac{74}{3}

= \frac{74}{3}