integral from 0 to 2 of xe-(x^2-1)/2

解答

\int_{0}^{2} x e - \frac{x ^{2} - 1}{2} d x

e 2 - \frac{1}{3}

十进制

5.10323 \dots

求解步骤

\int_{0}^{2} x e - \frac{x ^{2} - 1}{2} d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

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

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