What is the integral from-infinity to 0 of 7^r ?

The integral from-infinity to 0 of 7^r is 1/(ln(7))

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integral from-infinity to 0 of 7^r

\int_{- \infty}^{0} 7^{r} d r

\frac{1}{ln ( 7 )}

Decimal Notation

0.51389 \dots

Solution steps

\int_{- \infty}^{0} 7^{r} d r

Compute the indefinite integral:

\int 7^{r} d r = \frac{7 ^{r}}{ln ( 7 )} + C

Compute the boundaries:

\int_{- \infty}^{0} 7^{r} d r = \frac{1}{ln ( 7 )} - 0

= \frac{1}{ln ( 7 )} - 0

Simplify

= \frac{1}{ln ( 7 )}

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What is the integral from-infinity to 0 of 7^r ?
The integral from-infinity to 0 of 7^r is 1/(ln(7))