Example 2.25. $\int_{-\infty}^{0} e^{x} d x$.

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Example 2.25. $\int_{-\infty}^{0} e^{x} d x$.
Solution. According to formula (2.6), we get

$$
\int_{-\infty}^{0} e^{x} d x=\lim _{a \rightarrow-\infty} \int_{a}^{0} e^{x} d x=\left.\lim _{a \rightarrow -\infty} e^{x}\right|_{a} ^{0}=1
$$