What is the integral from-infinity to-3 of θe^θ ?

The integral from-infinity to-3 of θe^θ is -4/(e^3)

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integral from-infinity to-3 of θe^θ

\int_{- \infty}^{- 3} θ e^{θ} d θ

- \frac{4}{e ^{3}}

Decimal

- 0.19914 \dots

Solution steps

\int_{- \infty}^{- 3} θ e^{θ} d θ

Compute the indefinite integral:

\int θ e^{θ} d θ = e^{θ} θ - e^{θ} + C

Compute the boundaries:

\int_{- \infty}^{- 3} θ e^{θ} d θ = - \frac{4}{e ^{3}} - 0

= - \frac{4}{e ^{3}} - 0

Simplify

= - \frac{4}{e ^{3}}

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What is the integral from-infinity to-3 of θe^θ ?
The integral from-infinity to-3 of θe^θ is -4/(e^3)