What is the integral from-infinity to 0 of 4^x ?

The integral from-infinity to 0 of 4^x is 1/(2ln(2))

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integral from-infinity to 0 of 4^x

\int_{- \infty}^{0} 4^{x} d x

\frac{1}{2 ln ( 2 )}

Solution steps

\int_{- \infty}^{0} 4^{x} d x

Compute the indefinite integral:

\int 4^{x} d x = \frac{2 ^{2 x - 1}}{ln ( 2 )} + C

Compute the boundaries:

\int_{- \infty}^{0} 4^{x} d x = \frac{1}{2 ln ( 2 )} - 0

= \frac{1}{2 ln ( 2 )} - 0

Simplify

= \frac{1}{2 ln ( 2 )}

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What is the integral from-infinity to 0 of 4^x ?
The integral from-infinity to 0 of 4^x is 1/(2ln(2))