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Math Help - improper integrals

  1. #1
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    improper integrals

    lim as 2 approaches infinity \int_2^{inf} e^{-1.9x} dx

    the limit of integration infinity becomes b, and you have to apply the FTC to determine whether it's convergent/divergent etc.

    My answer for the integration alone is -1.9e^{-1.9x}. When I replace the x by 2 and evaluate, I get -0.0425. However I don't know what to do when doing the same thing with B as my value.

    This is what I'm left with; lim as 2 approaches infinity -1.9e^{-1.9b} - 0.0425

    How can I follow this up?
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  2. #2
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    Quote Originally Posted by Archduke01 View Post
    lim as 2 approaches infinity \int_2^{inf} e^{-1.9x} dx

    the limit of integration infinity becomes b, and you have to apply the FTC to determine whether it's convergent/divergent etc.

    My answer for the integration alone is -1.9e^{-1.9x}. When I replace the x by 2 and evaluate, I get -0.0425. However I don't know what to do when doing the same thing with B as my value.

    This is what I'm left with; lim as 2 approaches infinity -1.9e^{-1.9b} - 0.0425

    How can I follow this up?
    how does "2" approach infinity?

    learn the correct format for improper integrals ...

    \lim_{b \to \infty} \int_2^b e^{-1.9x} \, dx<br />

    \lim_{b \to \infty} \left[-\frac{e^{-1.9x}}{1.9}\right]_2^b

    \lim_{b \to \infty} -\frac{1}{1.9} \left[e^{-1.9b} - e^{-3.8}\right] = \frac{e^{-3.8}}{1.9} \approx 0.011774...
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  3. #3
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    Quote Originally Posted by skeeter View Post
    how does "2" approach infinity?

    learn the correct format for improper integrals ...

    \lim_{b \to \infty} \int_2^b e^{-1.9x} \, dx<br />

    \lim_{b \to \infty} \left[-\frac{e^{-1.9x}}{1.9}\right]_2^b

    \lim_{b \to \infty} -\frac{1}{1.9} \left[e^{-1.9b} - e^{-3.8}\right] = \frac{e^{-3.8}}{1.9} \approx 0.011774...
    Thank you!

    What I don't understand is why e^{-1.9b} is removed? It becomes infinity. What's the reasoning?
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  4. #4
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    Quote Originally Posted by Archduke01 View Post
    Thank you!

    What I don't understand is why e^{-1.9b} is removed? It becomes infinity. What's the reasoning?
    e^{-1.9b} = \frac{1}{e^{1.9b}}

    care to re-evaluate what you just stated?
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