What is the integral from-infinity to 4 of re^{r/2} ?

The integral from-infinity to 4 of re^{r/2} is 4e^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from-infinity to 4 of re^{r/2}

\int_{- \infty}^{4} r e^{\frac{r}{2}} d r

4 e^{2}

Decimal

29.55622 \dots

Solution steps

\int_{- \infty}^{4} r e^{\frac{r}{2}} d r

Compute the indefinite integral:

\int r e^{\frac{r}{2}} d r = 4 (\frac{1}{2} e^{\frac{r}{2}} r - e^{\frac{r}{2}}) + C

Compute the boundaries:

\int_{- \infty}^{4} r e^{\frac{r}{2}} d r = 4 e^{2} - 0

= 4 e^{2} - 0

Simplify

= 4 e^{2}

What is the integral from-infinity to 4 of re^{r/2} ?
The integral from-infinity to 4 of re^{r/2} is 4e^2