integral from 0 to 1 of e^y(e-1)

解答

\int_{0}^{1} e^{y} (e - 1) d y

(e - 1)^{2}

十进制

2.95249 \dots

求解步骤

\int_{0}^{1} e^{y} (e - 1) d y

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= (e - 1) \cdot \int_{0}^{1} e^{y} d y

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

= (e - 1) (e - 1)

化简

(e - 1) (e - 1) : (e - 1)^{2}

= (e - 1)^{2}

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