What is the integral from-infinity to 0 of ze^{7z} ?

The integral from-infinity to 0 of ze^{7z} is -1/49

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integral from-infinity to 0 of ze^{7z}

\int_{- \infty}^{0} z e^{7 z} d z

- \frac{1}{49}

Decimal Notation

- 0.02040 \dots

Solution steps

\int_{- \infty}^{0} z e^{7 z} d z

Compute the indefinite integral:

\int z e^{7 z} d z = \frac{1}{49} (e^{7 z} \cdot 7 z - e^{7 z}) + C

Compute the boundaries:

\int_{- \infty}^{0} z e^{7 z} d z = - \frac{1}{49} - 0

= - \frac{1}{49} - 0

Simplify

= - \frac{1}{49}

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What is the integral from-infinity to 0 of ze^{7z} ?
The integral from-infinity to 0 of ze^{7z} is -1/49