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人気のある微分積分 >

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

解

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

解

- \frac{1}{49}

+1

十進法表記

- 0.02040 \dots

解答ステップ

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

不定積分を計算する:

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

限度を計算する:

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

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

簡素化

= - \frac{1}{49}

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