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Math Help - divergent

  1. #1
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    divergent

    Determine whether the improper integral converges or diverges. If it converges, find the value.

    4e^4x at (-infinity. 0]
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  2. #2
    MHF Contributor red_dog's Avatar
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    \displaystyle\int_{-\infty}^04e^{4x}dx=\lim_{n\to\infty}\int_{-n}^04e^{4x}dx=\lim_{n\to\infty}\left(\left.e^{4x}\  right|_{-n}^0\right)=
    \displaystyle =\lim_{n\to\infty}(1-e^{-4n})=1
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