What is the integral from-infinity to 1 of e^{λt} ?

The integral from-infinity to 1 of e^{λt} is (e^λ)/λ

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integral from-infinity to 1 of e^{λt}

\int_{- \infty}^{1} e^{λ t} d t

\frac{e ^{λ}}{λ}

Solution steps

\int_{- \infty}^{1} e^{λ t} d t

Compute the indefinite integral:

\int e^{λ t} d t = \frac{1}{λ} e^{λ t} + C

Compute the boundaries:

\int_{- \infty}^{1} e^{λ t} d t = e^{λ} \frac{1}{λ} - 0

= e^{λ} \frac{1}{λ} - 0

Simplify

= \frac{e ^{λ}}{λ}

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What is the integral from-infinity to 1 of e^{λt} ?
The integral from-infinity to 1 of e^{λt} is (e^λ)/λ