Question

State true or false:

The value of the integral ${\int }_{-\infty }^{0}x.e^{x}dx$ is not finite.

• A. True
• B. False

Answer 1

The correct option is B False

${\int }_{-1}^{0}x{e}^{x}dx={\left[e^{x}x\right]}_{-1}^0-{\int }_{-1}^0{e}^{x}dx={[e^{x}x-e^x]}_{-1}^0=0-1+e^{-1}+e^{-1}={2e}^{-1}-1$