Answer
$$1000$$
Work Step by Step
$$\eqalign{
& \int_{ - \infty }^0 {1000{e^x}} dx \cr
& {\text{by the definition of an improper integral}}{\text{}} \cr
& \int_{ - \infty }^0 {1000{e^x}} dx = \mathop {\lim }\limits_{a \to - \infty } \int_a^0 {1000{e^x}} dx \cr
& = 1000\mathop {\lim }\limits_{a \to - \infty } \int_a^0 {{e^x}} dx \cr
& {\text{integrating}} \cr
& = 1000\mathop {\lim }\limits_{a \to - \infty } \left[ {{e^x}} \right]_a^0 \cr
& {\text{evaluate}} \cr
& = 1000\mathop {\lim }\limits_{a \to - \infty } \left( {{e^0} - {e^a}} \right) \cr
& = 1000\mathop {\lim }\limits_{a \to - \infty } \left( {1 - {e^a}} \right) \cr
& {\text{evaluating the limit when }}a \to - \infty \cr
& = 1000\left( {1 - {e^{ - \infty }}} \right) \cr
& = 1000\left( {1 - 0} \right) \cr
& = 1000 \cr} $$
