What is the integral from-infinity to 0 of e^{rx} ?

The integral from-infinity to 0 of e^{rx} is 1/r

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integral from-infinity to 0 of e^{rx}

\int_{- \infty}^{0} e^{r x} d x

\frac{1}{r}

Solution steps

\int_{- \infty}^{0} e^{r x} d x

Compute the indefinite integral:

\int e^{r x} d x = \frac{1}{r} e^{r x} + C

Compute the boundaries:

\int_{- \infty}^{0} e^{r x} d x = \frac{1}{r} - 0

= \frac{1}{r} - 0

Simplify

= \frac{1}{r}

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What is the integral from-infinity to 0 of e^{rx} ?
The integral from-infinity to 0 of e^{rx} is 1/r