Problem with improper integrals

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Homework Help Overview

The discussion revolves around evaluating the improper integral ∫xe^(-2x)dx from x = 0 to ∞, with participants exploring the steps involved in finding the correct value of the integral.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the evaluation of the integral, including the application of limits and the importance of considering both the upper and lower bounds. There is a focus on the substitution of limits and the resulting calculations.

Discussion Status

Some participants have identified mistakes in their calculations and are revisiting their steps. There is an acknowledgment of the need to correctly apply the limits in the evaluation process, with some guidance provided regarding the substitution of the lower limit.

Contextual Notes

Participants express confusion regarding the steps leading to the final result and the discrepancies between their calculations and external sources like Wolfram Alpha.

cesaruelas
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Homework Statement



∫xe^(-2x)dx from x = 0 to ∞

Homework Equations



-xe^(-2x)/2 - e^(-2x)/4 + C

The Attempt at a Solution



lim b→∞ -x/2e^(2b) - 1/4e^(2b) = 0

wolfram alpha says its 1/4 and I do not know why (it does not show steps)

Can you help me?
 
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You did not take the lower limit into account. Substitute x=0 and subtract.

ehild
 
You're right lol I'm dumb... anyway substituting the lower limit I get 3/4 and not 1/4 :/
-(-1/2 - 1/4) = 3/4
 
Thank you
 
just saw my mistake... 1/2 should be zero, that way I do get 1/4... thank you again
 

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