30. ∫_{-∞}^{0} e^x dx

Explanation:

Step1: Recall integral formula

The antiderivative of (e^{x}) is (e^{x}), i.e., (\int e^{x}dx=e^{x}+C).

Step2: Evaluate definite - integral

(\int_{-\infty}^{0}e^{x}dx=\lim_{a\rightarrow-\infty}\int_{a}^{0}e^{x}dx). First, (\int_{a}^{0}e^{x}dx=\left[e^{x}\right]{a}^{0}=e^{0}-e^{a}). Then, (\lim{a\rightarrow-\infty}(e^{0}-e^{a})=\lim_{a\rightarrow-\infty}(1 - e^{a})). Since (\lim_{a\rightarrow-\infty}e^{a}=0), we have (\lim_{a\rightarrow-\infty}(1 - e^{a})=1-0 = 1).

Answer:

1