What is the integral from-infinity to 0 of ze^{2z} ?

The integral from-infinity to 0 of ze^{2z} is -1/4

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integral from-infinity to 0 of ze^{2z}

\int_{- \infty}^{0} z e^{2 z} d z

- \frac{1}{4}

Solution steps

\int_{- \infty}^{0} z e^{2 z} d z

Compute the indefinite integral:

\int z e^{2 z} d z = \frac{1}{4} (e^{2 z} \cdot 2 z - e^{2 z}) + C

Compute the boundaries:

\int_{- \infty}^{0} z e^{2 z} d z = - \frac{1}{4} - 0

= - \frac{1}{4} - 0

Simplify

= - \frac{1}{4}

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(- 1, 2), (3, - 3)

What is the integral from-infinity to 0 of ze^{2z} ?
The integral from-infinity to 0 of ze^{2z} is -1/4