ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

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

解

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

解

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

+1

十進法表記

3.63918 \dots

解答ステップ

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

不定積分を計算する:

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

限度を計算する:

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

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

簡素化

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

人気の例

integral from-2pi to 2pi of xsin(0.5nx)

\int_{- 2 π}^{2 π} x sin (0.5 n x) d x

integral from 0 to 1 of (ln(x^2))/(x^2)

\int_{0}^{1} \frac{ln ( x ^{2} )}{x ^{2}} d x

integral from 0 to 2 of 3-(4e^{0.28t})/(e^{0.28t)+10.13}

\int_{0}^{2} 3 - \frac{4 e ^{0.28 t}}{e ^{0.28 t} + 10.13} d t

integral from 0 to 2 of k(4x-2x^2)

\int_{0}^{2} k (4 x - 2 x^{2}) d x

integral from 0 to 3 of (4x(9-x^2))/(81)

\int_{0}^{3} \frac{4 x ( 9 - x ^{2} )}{81} d x