integral from 0 to infinity of 4xe^{-4x}

解答

\int_{0}^{\infty} 4 x e^{- 4 x} d x

\frac{1}{4}

十进制

0.25

求解步骤

\int_{0}^{\infty} 4 x e^{- 4 x} d x

计算不定积分:

\int 4 x e^{- 4 x} d x = - e^{- 4 x} x - \frac{1}{4} e^{- 4 x} + C

带入上下限计算后得:

\int_{0}^{\infty} 4 x e^{- 4 x} d x = 0 - (- \frac{1}{4})

= 0 - (- \frac{1}{4})

化简

= \frac{1}{4}

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