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

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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}

\frac{d}{d x} (x^{2} + 5 x - 2)

\int - cos (2 θ) d θ

\frac{d y}{d x} = (x + y)^{2} + 1

\int - x^{2} + 4 d x

\frac{d ^{3}}{d x ^{3}} (cos (x))

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