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

The integral from-infinity to 0 of e^{ax} is 1/a

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

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

\frac{1}{a}

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= \frac{1}{a} - 0

Simplify

= \frac{1}{a}

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