A volume question with improper integral

Thread starter transgalactic
Start date Jan 24, 2008
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Improper integral Integral Volume

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SUMMARY

The discussion centers on the evaluation of the improper integral involving the function e^-2x. A participant challenges the misconception that e^-2x approaches infinity as x approaches infinity, clarifying that both e^-x and e^-2x actually converge to 0. The importance of accurately interpreting the behavior of exponential functions in limits is emphasized, particularly in the context of improper integrals.

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Understanding of improper integrals
Familiarity with exponential functions
Knowledge of limits in calculus
Graphing skills for visualizing function behavior

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Study the properties of improper integrals in calculus
Learn about the behavior of exponential functions as x approaches infinity
Explore techniques for evaluating limits involving exponential decay
Review graphing methods for visualizing function convergence

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Students studying calculus, educators teaching integral calculus, and anyone seeking to deepen their understanding of improper integrals and exponential functions.

Jan 24, 2008

transgalactic

i added a link with the question and how i tried to solve it

http://img167.imageshack.us/my.php?image=img8215vv0.jpg

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Jan 24, 2008

HallsofIvy

Science Advisor

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Where did you get the idea that e^-2x goes to infinity as x goes to infinity! Look at the graph you drew! e^-x, and certainly e^-2x, goes to 0 as x goes to infinity.