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

解答

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

\frac{6}{e ^{\frac{1}{2}}}

十进制

3.63918 \dots

求解步骤

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

计算不定积分:

\int x e^{- \frac{x}{2}} d x = - 2 e^{- \frac{x}{2}} x - 4 e^{- \frac{x}{2}} + C

带入上下限计算后得:

\int_{1}^{\infty} x e^{- \frac{x}{2}} d x = 0 - (- \frac{6}{e ^{\frac{1}{2}}})

= 0 - (- \frac{6}{e ^{\frac{1}{2}}})

化简

= \frac{6}{e ^{\frac{1}{2}}}

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