What is the integral from-infinity to 2 of (x-2)e^x ?

The integral from-infinity to 2 of (x-2)e^x is -e^2

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integral from-infinity to 2 of (x-2)e^x

\int_{- \infty}^{2} (x - 2) e^{x} d x

- e^{2}

Decimal

- 7.38905 \dots

Solution steps

\int_{- \infty}^{2} (x - 2) e^{x} d x

Compute the indefinite integral:

\int (x - 2) e^{x} d x = e^{x} x - 3 e^{x} + C

Compute the boundaries:

\int_{- \infty}^{2} (x - 2) e^{x} d x = - e^{2} - 0

= - e^{2} - 0

Simplify

= - e^{2}

What is the integral from-infinity to 2 of (x-2)e^x ?
The integral from-infinity to 2 of (x-2)e^x is -e^2