integral from 0 to 1 of xe^{x^2}-x

解答

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

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

十进制

0.35914 \dots

求解步骤

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

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

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

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

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