What is the integral from-infinity to 0 of ze^{6z} ?

The integral from-infinity to 0 of ze^{6z} is -1/36

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integral from-infinity to 0 of ze^{6z}

\int_{- \infty}^{0} z e^{6 z} d z

- \frac{1}{36}

Decimal Notation

- 0.02777 \dots

Solution steps

\int_{- \infty}^{0} z e^{6 z} d z

Compute the indefinite integral:

\int z e^{6 z} d z = \frac{1}{36} (e^{6 z} \cdot 6 z - e^{6 z}) + C

Compute the boundaries:

\int_{- \infty}^{0} z e^{6 z} d z = - \frac{1}{36} - 0

= - \frac{1}{36} - 0

Simplify

= - \frac{1}{36}

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What is the integral from-infinity to 0 of ze^{6z} ?
The integral from-infinity to 0 of ze^{6z} is -1/36