Solving an Improper Integral Problem: 1/(4x-2)^5 dx from 2 to infinity

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Homework Help Overview

The discussion revolves around evaluating an improper integral of the function 1/(4x-2)^5 from 2 to infinity. Participants are exploring the integration process and the expectations for presenting the answer.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the integration process and the resulting expression. There are questions about whether the answer should be presented as a fraction or a decimal, and some participants express frustration with online homework systems.

Discussion Status

Some participants have provided guidance regarding the format of the answer, suggesting that the original poster may need to submit the result as a fraction. There is acknowledgment of the challenges posed by online answer checking systems.

Contextual Notes

Participants note the potential for confusion regarding the format of the answer and the implications of online submission requirements. There is also mention of the original poster's integration attempt being perceived as incorrect by the system.

loganblacke
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Homework Statement


Find the value of Integral from 2 to infinity of 1/(4x-2)^5 dx.

Homework Equations





The Attempt at a Solution


When I integrated I came up with -(1/(16(2-4x)^4)), top - bottom which ends up being 0-(-.0004822) but it says that is wrong. Help please!
 
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That looks fine to me. Maybe they want the exact answer as a fraction instead of the decimal approximation?
 
Dick said:
That looks fine to me. Maybe they want the exact answer as a fraction instead of the decimal approximation?

Good call, that is exactly what they were looking for, 1/20736. Whoever decided calculus homework should be done online should be tortured.
 
loganblacke said:
Good call, that is exactly what they were looking for, 1/20736. Whoever decided calculus homework should be done online should be tortured.

Online answer checking in general is a pain in the neck. It has no idea whether you are right or wrong, just whether it fits whatever form it's set to recognize. I sympathize.
 
loganblacke said:
When I integrated I came up with -(1/(16(2-4x)^4)), top - bottom which ends up being 0-(-.0004822) but it says that is wrong.

There should be four 0's after the decimal point: 0.000048225308641975306 ≈ 1/20736
So make sure your enter your number correctly when submitting it online. :wink:
 

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