What is the integral from-infinity to 16 of re^{r/4} ?

The integral from-infinity to 16 of re^{r/4} is 48e^4

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integral from-infinity to 16 of re^{r/4}

\int_{- \infty}^{16} r e^{\frac{r}{4}} d r

48 e^{4}

Decimal

2620.71120 \dots

Solution steps

\int_{- \infty}^{16} r e^{\frac{r}{4}} d r

Compute the indefinite integral:

\int r e^{\frac{r}{4}} d r = 4 e^{\frac{r}{4}} r - 16 e^{\frac{r}{4}} + C

Compute the boundaries:

\int_{- \infty}^{16} r e^{\frac{r}{4}} d r = 48 e^{4} - 0

= 48 e^{4} - 0

Simplify

= 48 e^{4}

What is the integral from-infinity to 16 of re^{r/4} ?
The integral from-infinity to 16 of re^{r/4} is 48e^4