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Solution assignment 01 Improper integrals

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Assignment 1

Calculate:

\displaystyle\int_{-\infty}^{0}{e^x}dx

Solution

The calculation is straightforward:

\displaystyle\int_{-\infty}^{0}{e^x}dx=

=\displaystyle\lim_{a\to{-\infty}}\int_{a}^{0}{e^x}dx=

=\displaystyle\lim_{a\to{-\infty}}[e^x]_{a}^{0}=1

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