integral from 3 to infinity of e^{-x/4}

解答

\int_{3}^{\infty} e^{- \frac{x}{4}} d x

\frac{4}{e ^{\frac{3}{4}}}

十进制

1.88946 \dots

求解步骤

\int_{3}^{\infty} e^{- \frac{x}{4}} d x

计算不定积分:

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

带入上下限计算后得:

\int_{3}^{\infty} e^{- \frac{x}{4}} d x = 0 - (- \frac{4}{e ^{\frac{3}{4}}})

= 0 - (- \frac{4}{e ^{\frac{3}{4}}})

化简

= \frac{4}{e ^{\frac{3}{4}}}

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